Selectivity hplc para liquidos y gases by RAU MORILL

CHAPTER 3

PARAMETERS AFFECTING SELECTIVITY Before starting any optimization process, we should ask ourselves what exactly it is we want to optimize. In general terms our goal is to obtain the best possible chromatogram for a particular purpose. In the next chapter we will discuss criteria by which to judge the quality of a chromatogram. In the present chapter, we will describe the parameters that influence retention and selectivity, and see which parameters we might consider (or exploit) during the optimization process. Where possible, we will derive simple relationships between retention and the relevant parameters. For reasons of clarity, we will express all equations in terms of the capacity factor (k).Obviously, the simplest possible equations will be most useful for optimization purposes. Ideally, we will be looking for linear relationships, since straight lines allow straightforward interpolation. At the end of the chapter (section 3.5) we will summarize the relationships that are recommended for the various parameters in different kinds of chromatography. 3.1 GAS CHROMATOGRAPHY 3.1.1 Gas-liquid chromatography (GLC) In this form of chromatography retention can readily be expressed in thermodynamic terms. The definition equation for the capacity factor ( k ) is

where q i is the total quantity of the solute in either phase, Ci the average solute concentration and Y the total volume of the indicated phase in the column. If we assume very dilute solutions (as is usually the case in chromatography), we can write for the concentration in the stationary phase

where xi,sis the mole fraction of the solute in the stationary phase, and p, and M, are the density and the molecular weight of this phase, respectively. For the mobile (gaseous) phase we can write = l/vi,m =

Pi ~

â&#x20AC;&#x2122;

(3.3)

where vi,,, is the partial molar volume of the solute in the gaseous phase, p i its partial pressure, and (= p i vi,,, / R T ) the compressibility coefficient. Since we are dealing with gases at low pressures, we may usually (and definitely for the present purpose) assume the ideal gas law to be valid. Hence, we may assume to be equal to one. 37

For dilute solutions, we may use Henry’s law to describe the partial pressure of the solute:

where is the activity coefficient (at infinite dilution) of the solute in the stationary phase and py is the vapour pressure of the pure solute. Hence, for the ratio of concentrations we find from eqn~(3.2)to (3.4):

Because this ratio is independent of the concentration of the solute, it equals the ratio of the average concentrations, and hence

where ns is the total number of moles of the stationary phase present in the column. From eqn.(3.6) we conclude that there are two solute-dependent factors that affect retention. In the first place, this is the vapour pressure of the pure solute. p? is a strong function of the temperature (see below) and therefore, temperature may be used as a parameter to influence retention. However, the vapour pressure is a pure component property and it cannot be changed at will. Differences in the vapour pressure of two solutes (or differences in variation of vapour pressure with temperature) may or may not provide us with a means to achieve separation. When the vapour pressure is not sufficiently different, we need to create differences in the second solute-dependent factor. This is the activity coefficient of the solute in the stationary phase (rf“,). The value of 7 is determined by molecular interactions between the solute and the stationary phase. Therefore, (chemically) different stationary phases will lead to different values for 7. This explains the availability of many different stationary phases for GC, many of which show different selectivity (see section 2.3.2).

Temperature Eqn.(3.6) provides a good insight into the variation of retention with temperature in GLC. Both the activity coefficient and the vapour pressure of the solute vary with temperature in an exponential way. For the activity coefficient we can write In

es= h d R T - s d R ,

(3.7)

where h , and s E are the (partial molar) “excess” enthalpy and entropy respectively*. The vapour pressure can be approximated with the common Clausius-Clapeyron equation:

* The excess quantities measure the deviation of the solution of i in s from the “perfect”solution, for = 1. which Raoult’s law is obeyed, i.e.

Inpp = h , / R T - s , / R , where h, and s, are the molar heat and entropy of vaporization. If we now combine eqns.(3.6), (3.7) and (3.8) we find

h,+ h" + S E + % + I nRn s , I n k = In T - RT R Vrn i.e. an equation of the form

(3.9)

(3.10)

Ink=lnT+A/T+ B

where A and B are constants. According to this equation, we can expect to obtain a straight line if we plot In (k/ T) versus 1/ T. This somewhat odd-looking relationship corresponds to the more common procedure of plotting the logarithm of the specific retention volume ( Vg) against the reciprocal temperature. Vgis defined as the net retention volume at standard temperature (0 "C) and per unit weight of stationary phase: (3.1 1) Figure 3.1 provides an illustration of the relationship between the specific retention volume and the temperature. A great disadvantage of using V, is that ws is not usually known. Alternatively, we may write eqk(3.10) as Tln(k/T) = A

1.01

(3. I Oa)

10'IT

Figure 3.1: Example of the linear dependence of the logarithm of the specific retention volume (eqn.3.11) on the reciprocal temperature. Stationary phase : silicone oil 702. Solutes: n-alcohols (number of carbon atoms as indicated in the figure). Figure taken from ref. [301]. Reprinted with permission.

(a)

Figure 3.2 Fundamental linear relationship between retention and temperature in GLC according

to eqn.(3.l0b). Stationary phases: (a) SE-30 (silicone oil) and (b) Carbowax 20M (polyethylene-gly-

col). Solutes: n-alkanes (number of carbon atoms as indicated in the figure). Figure taken from ref. [302]. Reprinted with permission.

or, because k is proportional to the net retention volume Vx, Tln(VR/T) = A‘

+ B’T.

(3.10b)

where A’ and B’ are constants. Figure 3.2 shows an example of a plot according to eqn. (3.10b). The linearity of these plots is clear.

The stationary phase The properties of the stationary phase manifest themselves in the activity coefficient in eqn.(3.6). A very simple expression for the activity coefficient can be obtained from the concept of solubility parameters (see section 2.3.1). This expression can be seen as a special form of Hildebrand’s regular mixing rule, and it reads [303]. In

cs= ( V / R T )(6i- 6b2 + In ( v i / v s ) + (1 - v / v > ,

(3.12)

where the subscript i denotes the solute, and s denotes the stationary phase. v is the molar volume. The first term on the right hand side of eqn.(3.12) is the enthalpic (“regular”) contribution to the activity coefficient. The other two terms together form the entropic (“athermic”) part. Unfortunately, this very simple equation does not usually yield quantitatively reliable results, unless, perhaps, for the interaction of solutes of low-polarity with phases of low polarity. However, eqn.(3.12) does provide us with a simple means to explain and understand the role of the “polarity” of solutes and stationary phases in GLC. Almost always, the enthalpic contribution dominates the right hand side of eqn.(3.12), in which case we can use the approximate expression 40

= (vi/R7‘) (Si- SJ’.

(3.13)

Clearly, the right-hand side of eqn.(3.13) is always positive. Consequently, it leads to activity coefficientswhich are above unity, and hence (since the capacity factor is inversely proportional to y) towards decreasing retention. When the polarity of the solute and the stationary phase are similar, then only the (small and negative) entropic contribution to the activity coefficient will remain, y will be close to unity, and retention will mainly be determined by the pure solute’s vapour pressure. The vapour pressure, in its turn, is closely related to the boiling point. Indeed, this case is often encountered in the GLC of low polarity solutes on low polarity stationary phases (“boiling point separation”). Because of the occurrence of the excess quantities h , and sEin eqn.(3.9), the coefficients in eqn.O.10) for the temperature dependence of the retention are a function of the stationary phase. Hence, every stationary phase may be expected to yield a different optimum temperature, at which the capacity factors of all sample components fall in the optimum range. Therefore, to make a fair comparison between two different stationary phases for a given separation problem*, the (potentially different) optimum temperature should be established for each of them and the resulting chromatograms should be compared. The common practice of characterizing (and consequently comparing) stationary phases at a standard temperature is a very convenient one. Nevertheless, it may give rise to erroneous conclusions in some cases.

Mixed stationary phases The choice of a stationary phase is no longer a discrete variable once mixtures of stationary phases are considered. For binary mixtures the following relationship is usually observed** (3.14) where cp denotes the volume fraction, and the subscripts A and B represent two different stationary phases. According to eqn.(3.14) a mixture of two stationary phases behaves as the sum of two individual contributions. The same result may be obtained using a 50150 mixture of the two phases A and B, as with two similar columns (of half the original length) coated with pure A and pure B, respectively, coupled in series. Indeed, in practice both methods may have certain advantages. Figure 3.3 shows an example of a plot of the retention in GLC versus the composition of the stationary phase. In this and many other cases straight lines are observed. Figure 3.4 shows an exceptional case, in which no straight lines were observed. Eqn.(3.14) is usually, but not always obeyed in practice. Moreover, it is hard to predict when deviations will occur. Apparently [306], not only the two stationary liquids involved,

* For some suggestions on how to select different stationary phases see section 2.3.2.

It should be noted that eqn.(3.14) applies only when the total volume of the stationary phase is kept constant.

'PDNP

Figure 3.3: Variation of retention (distribution coefficient) with the composition of the stationary phase in GLC at three different temperatures (indicated in the figure in "C). Stationary phase: mixtures of squalane and dinonylphthalate (DNP). Solutes: (a) n-octane, (b) cyclohexane, (c) methylcyclohexane and (d) tetrahydrofuran. Straight lines observe eqn.(3.14). Figure.taken from ref. [304]. Reprinted with permission.

500

\'\\ '\f\

L 20

630

580

130

0.5 PDNP-

0.5 'PDNP

Figure 3.4 : Variation of retention (distribution coefficient) with the composition of the stationary phase in GLC. Stationary phase: mixtures of squalane and dinonylphthalate (DNP). Solutes: (a) cyclohexane, (b) methylcyclohexane, (c) benzene, and (d) toluene. Temperature: 30 OC. Curved lines are obtained, which do not obey eqn.(3.14). Figure taken from ref. [305]. Reprinted with permission.

but also the procedure that is used to form the mixture and to coat the mixture on the column is relevant in this respect. Nevertheless, eqn.(3.14) may be assumed valid, until there are indications to the contrary. After eqk(3.14) turned out to be obeyed by many systems in practice, a model was developed that could provide a physical picture. This so-called diachoric model [306] explains the fact that the two components of the mixed phase behave independently by demixing on a microscopic scale. Hence, the stationary phase is assumed to consist of little patches or droplets of either pure A or pure B. Obviously, such a model does explain obeyance of eqn.(3.14), while it also gives a handle to explain deviations from linearity in terms of complete mixing of the two phases. It is useful at this point to realize that with the composition of the stationary phase being a continuous variable and with retention and selectivity being strong functions of temperature, the optimum composition may also be expected to vary with temperature. Ideally therefore, temperature and stationary phase composition should be optimized simultaneously (see section 5.1.1). Moreover, once different lengths of columns with the individual stationary phases are applied instead of real mixtures, it is in theory feasible to optimize the temperature of each of the columns, as well as the ratio of column lengths simultaneously.

3.1.2 Gas-solid chromatography We can describe the retention behaviour in GSC in similar terms as we did for GLC in the previous section. However, we have to reconsider our definitions of the concentration in the stationary phase and of the distribution coefficient. It is common practice to express the concentration of the solute adsorbed onto the stationary phase in terms of moles per gram of adsorbent, i.e.

= 4JWS

(3.1 5)

where w, is the weight of the sorbent present in the column. Therefore, the partition coefficient

K = -c:- ?-C

Vrn 4rn

(3.16)

is now expressed in units of ml/g. An expression for Henry's adsorption law can be formulated that is analogous to eqn.(3.4) [307]:

4, = Hi A , Pi

(3.17)

where Hi(units: mol.atm-'.m-*) is Henry's adsorption coefficient for the solute ion the solid adsorbent. Hi is determined mainly by the interactions between the stationary phase and the solute, and hence it takes over the role of the activity coefficient in GLC. Note that the vapour pressure of the pure solute does not appear as an independent entry in eqn.(3.17). A, is the surface area of the adsorbent. Using eqn.(3.3) with = 1 for the mobile phase, we find from a combination of eqns.(3.15), (3.16) and (3.17) that K , = Hi A, R T / w, =

HisR T ,

(3.18) 43

where s is the surface area per unit weight of the adsorbent (m2/g), usually called the specific surface area. The capacity factor now becomes (3.19) and finally for the relative retention:

aI.', . = k / k , = HfH,.

(3.20)

Hence, the selectivity in GSC is determined by the values of the Henry adsorption coefficients of the two solutes. Eqn.(3.19) describes the ideal case in which the adsorption isotherm of the solute is linear and the carrier gas does not adsorb onto the stationary phase. This simple situation is not always encountered, but analytical equations can be derived for many other cases [308]. In fact, the practical conditions in GSC are more often non-ideal than is the case in GLC. The adsorption isotherm can only be approximated as linear at very low concentrations. In other words, solute capacities are usually lower in GSC. Surface heterogeneities play a role, especially on inorganic adsorbents such as silica and alumina. These stationary phases are also sensitive to contaminations. Consequently, the observed peak shapes and retention times may be affected by the history of the column ("conditioning") and by the water content of the carrier gas. Because the pure component vapour pressure is not one of the determining factors for retention in GSC (eqn.3.19), GSC is especially useful for the separation of permanent gases and other solutes of low molecular weight. Even at room temperature the interaction with the stationary phase may be high enough to retain permanent gases on GSC columns. Under GLC conditions a reasonable retention for compounds with a very high vapour pressure is only possible if activity coefficients can be achieved that are very much smaller than one, and this is not a common situation. Because of the specific application area of GSC in the world of small molecules, the number of components to be separated is usually small. For most practical problems, therefore, specific stationary phases are readily available. Hence, GSC is not the most fertile soil for selectivity optimization. Temperature

The temperature of the column is the most important parameter in GSC. Its effect on retention can be described by the same equations as were used in GLC, as can be seen from a comparison of eqm(3.6) and (3.19). According to eqn.(3.10) a straight line will be obtained by plotting In (k/ 7 ) vs. (1 / 7). However, a plot of In k(or In VR)vs. the reciprocal temperature also yields approximately straight lines, as is illustrated in figure 3.5. Other parameters

Apart from the temperature, the only other factor that may affect the retention and selectivity in GSC is the nature and, theoretically,the composition of the stationary phase.

Figure 3.5 : Variation of retention (net retention volume per unit surface area of stationary phase) with the temperature in GSC. Stationary phase: GTCB (carbon). Solutes: o/p-xylene (l), m-xylene (2), n-octane (3), ethylbenzene(4), toluene (5), n-heptane (6), methylcyclohexane(7), exo-5-methylnorbornene (8), endo-5-methylnorborner1e(9),norbornane (10) and norbornene (1 1). Figure taken from ref. [309]. Reprinted with permission. The materials that can be used vary from inorganic oxides such as silica and alumina to organic polymers such as styrene-divinylbenzene copolymers. The inorganic materials are more stable at higher temperatures. Both silica and alumina are strongly affected by the water content of the surface. Therefore, the reproducibility and the repeatability of the separation largely depend on the â&#x20AC;&#x153;conditioningâ&#x20AC;? (equilibration) of the column. Alumina shows a remarkable affinity to hydrocarbons. For this reason it is eminently suitable for the separation of volatile hydrocarbon fractions, including alkane isomers up to about 5 carbon atoms. Due to both the magnitude of the interactions with the surface, as well as to the surface heterogeneity, both alumina and silica are less useful for the separation of polar compounds. This latter effect is not encountered to the same extent when organic (solid) polymers are used as the stationary phase. Hence, more or less polar substances with a high volatility may be eluted from such columns as symmetrical peaks. Mixed beds of stationary phases in a single column have not found much application in GSC. However, for the separation of complex gas mixtures, more than a single column is often used in a configuration that involves switching valves, so that only part of the sample is subjected to a second column (see also section 6.1). 3.1.3 The use of retention indices

â&#x20AC;&#x2DC;The retention index ( I ) was introduced in section 2.3.2 as a reproducible means for reporting CC retention data. The retention index was therefore found to be highly useful as the basis for a characterization scheme for stationary phases in GLC. In this chapter, however, the capacity factor and not the retention index has been used to find expressions, which describe the influence of the various relevant parameters on the retention. Besides 45

the fact that the use of capacity factors is consistent with other sections in this chapter, there is also a more fundamental reason behind this choice. The definition of the retention index in terms of capacity factors is In k,-In k, (3.21) I = 100 [ n + In k,+ -In k,

I-

If we use eqn.O.10) for the variation of the capacity factor with the temperature we find (3.22) In eqns(3.21) and (3.22) i denotes the solute and n and n + 1 the preceding and the following n-alkane, respectively (see figure 2.2). It is seen that there is a hyperbolic relationship between the retention index and the temperature. Although over small sections of the hyperbola a linear approximation is often used, this is not a sound basis for temperature optimization, especially not since a straight line can easily be obtained by plotting In ( k / vs. 11T (eqn.3.10). An even more complicated result is obtained if we express the retention index as a function of the stationary phase composition. A combination of eqm(3.14) and (3.21) (3.23) (a1

1210 -

LO 60 80 100 % Polybutadiene

LO 60 80 % Polybutadiene

100

Figure 3.6 : Variation of retention with the composition of the stationary phase in GLC. Stationary phase: styrene-butadiene polymer blends and copolymers, the butadiene fraction is plotted on the horizontal axis. (a) Specific retention volumes for three n-alkanes and benzene. V is proportional to the capacity factor. (b) the retention index for benzene. The solid line is calculated from the straight lines in figure 3.6a. The circles (polymer blends) and triangles (copolymers) represent experimental data. Figure taken from ref. [310]. Reprinted with permission. 46

Figure 3.6 illustrates the variation of (a) the specific retention volume ( Vg which is proportional to the capacity factor) with the composition of a mixed stationary phase, and (b) the variation of the retention index for benzene with the composition. It is clear from these figures that, whereas straight lines are observed for the variation of the capacity factor with the composition, the retention index varies in a highly non-linear manner. Clearly, for the purpose of selectivity optimization, the capacity factor ( k ) is greatly to be preferred to the retention index (I).

3.2 LIQUID CHROMATOGRAPHY We will first approach liquid chromatography by assuming that both phases are bulk fluids (i.e. LLC), and generalize our approach later. For LLC we can define a thermodynamic equilibrium constant ( K t h )as (3.24) i.e. the ratio of the solute activities in the two phases. A suitable standard state (at which by definition a = 1) should now be defined for each phase. As long as we strictly observe this definition, we are free to choose a convenient one. Hence, we opt for the pure solute i as standard state for both phases*, since in that case the activities are equal at unit concentration (1 00% i), and therefore at all concentrations: (3.25) and, using the definition for the activity coefficient (3.26) For the high dilutions encountered in LC this can be transformed into (3.27) where q is the amount of solute i (in number of moles) present in either phase. Finally, by definition (3.28)

* 'This definition is equivalent to the one implicitly assumed in Henry's law (section 3.1.1). An alternative way to arrive at eqm(3.25) is to consider the thermodynamic potential (p).A condition for equilibrium is that p should be equal in the two phases of a chromatographic system for each compound. Therefore, we can write for the solute pi,s = p!s

+ R T In aLs = pi,m = p!m +

R T In ai,m

Eqn.(3.25) follows immediately from this equation, if we again choose for the same standard state (the pure solute) in both phases (i.e. pys=py,,).

The last factor on the right-hand side of eqn.(3.28) is clearly a phase ratio, independent of the solute. Hence, the activity coefficients determine retention in liquid chromatography. In other words, retention is determined by the molecular interactions of the solute with the stationary and with the mobile phase. This situation is fundamentally different from the one in GC, where interactions with the stationary phase and the vapour pressure of the pure solute were the relevant factors (see section 3.1.1). In LC, both the interactions in the mobile phase and in the stationary phase can be influenced in order to optimize the selectivity of the system, and neither is beyond control in the sense that vapour pressure is in GC. The activity coefficient can be expressed in terms of solubility parameters (eqn.3.12). Neglecting the (small) entropy correction terms we find In ki = ( v / R T ) { (ai- 6,J2-(Si - 6J2} = ( v / R T ) {(6,+6, - 26,)(6,-6,)}

+ In(n,/n,J + ln(n/n,J.

(3.29)

The above equation is very approximate. It involves many assumptions and approximations [311], and it is not adequate for a quantitative description or prediction of retention in LC. However, because of its simplicity, it provides us with a very elegant means to explain many of the features of modem LC in qualitative terms. Since eqn.(3.29) will not be used quantitatively, we may take some additional liberties by assuming that it not only provides us with some insight into LLC systems, but may also be used for the qualitative interpretation of other forms of LC, notably LSC and LBPC as well. Indeed, this is not a new appproach, and a value for the solubility parameters of some solid surfaces has been suggested in the literature [303,312].

Retention According to eqn.(3.29) retention (k) varies exponentially with the polarity of the solute

(ai).It can easily be seen from eqn.(3.29) that as soon as the solubility parameter product

+ 6, - 26,)(6, - 6,) becomes significantly positive or negative, the capacity factor will either be impractically high or uselessly low. Hence, to a first approximation reasonable values for k will be obtained when the above product is about equal to zero. This can be achieved in two ways: 1. Choosing the mobile and the stationary phase of roughly the same polarity (i.e. 6, M 6,). While this has the desired effect on retention, the remedy is equally effective for all solutes, independent of the value of 6 ,and therefore it creates a very non-selective phase system (see the discussion on selectivity below). 2. Alternatively, the first factor can be minimized, by taking the solute polarity to be roughly intermediate between the polarities of the two phases: (6,

Si M (6, + &,)I2 .

(3.30)

This very simple rule of thumb for the selection of LC phase systems (a phase system is a combination of a mobile and a stationary phase) is illustrated in figure 3.7. In figure 3.7 three horizontal axes have been drawn, representing (from top to bottom) the solubility parameter of the stationary phase, the solute and the mobile phase. Each 48

n-alkylphases fluoroalkcines

silica

25 calv?cm-3’2 reversed phase

straight phase

T metianol alkanes THF acetonitrile

water

Figure 3.7: Illustration of the selection of phase systems for LC according to eqn.(3.30). A solute with a polarity of 12.5 (middle scale) can be eluted from silica (S,= 16; top scale) with a non-polar mobile phase (Sm=9; bottom scale) or with a polar solvent in a reversed phase system. The shaded areas indicate the latitude with respect to the selection of the mobile phase. Figure taken from ref. [311]. Reprinted with permission.

(non-horizontal) line in figure 3.7 represents a phase system for which eqm(3.30) is obeyed. Clearly, a vertical line again denotes a system for which the polarities of the two phases are equal. According tp the above discussion this is a completely non-selective phase system. In figure 3.7 two lines have been drawn, which represent two examples of possible phase The line with a positive systems for the elution of a solute with Si= 12.5 (cal”*.~m-~’~). slope connects a moderately polar mobile phase (6, = 9) with a polar stationary phase (a,= 16). Because the polarity of the stationary phase exceeds that of the mobile phase (a,:> S,), this is by definition a normal (or straight) phase system. ), and The reverse is true for the line drawn in figure 3.7 with a negative slope (a,< ,a for this reason this system is called a “reversed phase” (RP) system. The particular line in figure 3.7 connects a typical non-polar (alkane-like) phase with 6,= 7 to a polar mobile phase with 6,= 18. Such a mobile phase could for instance be created by mixing methanol ( 6 16) ~ with water ( 6 ~ 2 5in) the correct proportions. Since a very wide range of mobile phase polarities can be covered with mixtures of methanol and water, or even tetrahydrofuran (THE 6 s 10) and water, the reversed phase system is a very flexible one. Without changing the column (stationary phase), it can be applied for the elution of a wide variety of solutes. Alongside the two lines drawn in figure 3.7 as examples for phase systems, dotted areas are indicated towards the mobile phase axis. This is done to indicate that, when eqn.(3.30) is strictly obeyed, a small capacity factor is expected to result. By choosing the mobile phase polarity slightly further away from that of the solute, the capacity factor can be moved into the optimum range. However, the margin thus created is usually very small and 49

eqn.(3.30) may serve as a good (albeit qualitative) indication of the behaviour of LC systems. Selectivity From eqn.(3.29) a very simple expression for the selectivity of a phase system may be derived. For the relative retention (aj.>of two solutes with similar molar volumes ( v i = vj) we find In aj.i = In kj - In ki = (2vi/R7')(Si-Sj) (6,-Ss).

(3.31)

Hence, if we want to separate a given pair of solutes (i.e. Si and are fixed), the general approach involves maximizing the only variable left to control in eqn.(3.31), the factor

(6, - as)*.

By definition, the relative retention is larger than (or equal to) 1. Thus, for a normal phase system, where Ss>S , it followsfrom eqm(3.31) that Sj> 6 ,and hence themore polar solute will elute last. Again, the reverse is true for a reversed phase system. Becausethe signs of the two factors in eqn.(3.31) which involve solubility parameters will always be the same, we may state that it is the absolute difference between the polarities of the two phases that should be maximized. Therefore, the selectivity of a phase system ( V ) may be defined as (3.32)

Unfortunately, we cannot just use any combination of phases that would constitute a very selective phase system. For example, we might want to opt for the combination of an RPLC column with typically 6,yz7, with pure water (a= , 25.5) as.the mobile phase, which would result in a selectivity ( V ) of about 18. However, in this particular phase system only a very polar solute with 6,s16 would satisfy eqm(3.30). It will come as no surprise that in this particular (highly selective) phase system all but the very polar solutes will have extremely high capacity factors. In fact, for a given solute, once a given column (stationary phase) has been selected, the appropriate mobile phase can readily be obtained from eq~(3.30)(or graphically from figure 3.7). From a substitution of eqm(3.30) in eqn.(3.32) we find

= 2 (6, - 6.J .

(3.33)

This equation shows that we should ideally select a stationary phase with a polarity that is very different from that of the solute. Indeed, the recommendation to use normal phase chromatography (high S,J for non-polar solutes (low Si) and reversed phase chromatography (low 6.J for the separation of polar solutes (high Si) is not new. However, this rule of thumb is much too simple. A complication is caused by the availability of appropriate mobile phases. For instance, to satisfy eqn.(3.30) for the elution of non-polar solutes ( 4 ~ 7 from ) a silica column (6,yz16), a mobile phase with 6,- - 2 would be required.

* This factor can easily be shown to be of equally great importance for the separation of two molecules with similar polarities but with different molar volumes. 50

Clearly, this is an impossible proposition. Practical mobile phase polarities will be restricted to the range between 6,w7 (for alkanes) and 6, = 25.5 (for water). For some selected stationary phases, the selectivity that can be achieved as a function of the solute polarity is shown in figure 3.8. Eqn.(3.33) forms the basis for this figure, but the practical limits for the mobile phase polarity are respected. For example for a reversed phase column (represented by the line AT in figure 3.8 and denoted by the letters RP) the maximum solute polarity is just over 16 when pure water is used as the mobile phase. Phases with intermediate polarity are represented in figure 3.8 by a set of two lines in a V-shape. The set of lines denoted by LSC represents a typical normal phase adsorption material with a polarity of around 16 [312]. This stationary phase can be combined with a less polar mobile phase down to 6 , = 7, yielding the line with a negative slope in figure 3.8. This branch represents the common application of normal phase adsorption chromatography. However, the polar adsorbent may also be combined with an even more polar mobile phase up to a mobile phase polarity of 25.5 and a solute polarity of about 21. Hence, this line with positive slope in figure 3.8 represents the use of polar adsorbents in the reversed phase mode for the separation of very polar solutes. Interestingly enough, according to figure 3.8, the non-polar stationary phase (reversed phase column) will always lead to a higher selectivity than the more polar stationary phase (normal phase column), apart from the range for very polar solutes, where the polar stationary phase is used in the reversed phase mode. Indeed, there has been a recent interest in separations of this kind on silica, and some polar chemically bonded phases (see section 3.2.2) are especially useful in this respect. The separation of sugars on an amino-type column is a good example. The line TW in figure 3.8 is dashed. This is the virtually non-existent situation where water is being used as the stationary phase. Although this suggestion is not at all practical, it is clear from figure 3.8 that a very high selectivity could be obtained for polar solutes.

Figure 3.8 :Calculated selectivities according to eqn. (3.33) for various stationary phases as a function of solute polarity. RPF = perfluorinated reversed phase; RP = reversed phase; PC = pyrocarbon; LSC = alumina, silica. Figure taken from ref. [31 I]. Reprinted with permission.

Therefore, it seems an interesting challenge to try and create stationary phases of a polarity much higher than that of silica. There are two other phases indicated in figure 3.8. The first is a so-called pyrocarbon material. Such a stationary phase is formed by pyrolizing an organic layer on a silica substrate. The idea is to combine the mechanical strength of silica with the chemical inertness of carbon. The value of 14 used here can be thought of as typical for carbonaceous materials. These materials do not seem to behave like non-polar phases in the tradition of chemicallybonded phases for RPLC, but rather like phases of intermediate polarity. Hence, as for silica, they may be most useful in the reversed phase mode for the separation of very polar molecules using aqueous mobile phases. The thin line in the top left of figure 3.8 denoted by RPF represents a very non-polar perfluorinated (chemically bonded) stationary phase. Perfluorinated alkanes are known to behave like even less polar materials than the alkanes themselves 1313). Although it is theoretically possible to use such materials as a mobile phase (for instance for the separation of low polarity solutes on a silica column), figure 3.8 suggests that it will be more rewarding to use perfluorinated materials as the stationary phase. Of course, this proposition would also be more cost effective. Indeed, such materials have been studied by several researchers. The general conclusion of these studies turns out to be that there might be an overall increase in selectivity relative to conventional RPLC systems, but that this effect is overshadowed by very large specific effects (i.e. selectivity towards specific solutes)[314].Therefore, perfluorinated materials should be seen as alternative rather than as superior stationary phases for RPLC. The behaviour of the perfluorinated phases as discussed above illustrates the fact that the solubility parameter model, despite its charms, may only be used as a crude approximation. The occurrence of specific deviations from the general rule may at least be made plausible by differentiating between different kinds of molecular interactions, and by introducing so-called partial solubility parameters or partial polarities [303,3121 (see also section 2.3.1). However, such an extension greatly increases the complexity of the model, without increasing its predictive value correspondingly. 3.2.1 Liquid-liquid chromatography A liquid-liquid system can be created by coating a particulate matter with a thin layer of a liquid phase, similar to the way packed columns are used in GLC. To maintain such an LLC column, the stationary phase should be insoluble in the mobile phase, just as GLC phases need to be involatile at the temperature of operation. Unfortunately, â&#x20AC;&#x153;insolubilityâ&#x20AC;? is an absolute demand that can at best be approximated in practice. The solubility of the stationary phase in the mobile phase becomes even more critical once some flexibility is desired with regard to the choice of the mobile phase. For example, mixtures of several pure solvents are usually required in order to adapt the eluotropic strength (polarity) of the mobile phase such that the capacity factors fall in the optimum range. Because complete immiscibility of the two phases cannot usually be accomplished, practical measures will have to be taken to avoid bleeding of the stationary phase from the column, for example pre-saturation of the eluent with the stationary phase or the inclusion of a small coated column (coated with the same stationary phase as the analytical

column) in the flow stream before the injector. Basically, both the above remedies are very similar. Despite such measures, LLC columns with “insoluble” stationary phases are not very stable, for instance due to a disturbance of the system every time a sample is injected. The reproducibility of retention data on these LLC columns is generally unsatisfactory, and ‘‘aging” of the column tends to occur rapidly. Apparently, the stationary phase is not merely dissolved from the column because of its “solubility” in the mobile phase, but it may also be eroded from the column because of mechanical processes (shear forces) or by a solution-precipitation mechanism, which causes the stationary phase to be redistributed within the column. These effects may be enhanced by temperature changes within the column, due to viscous ‘heat dissipation and inadequate temperature control. Indeed, thermostatting of the column (and the eluent reservoir) is vital for the proper operation of LLC systems. Another problem associated with LLC is that of mixed retention mechanisms. Ideally, the solid support in LLC binds the molecules of the stationary phase with strong adsorptive forces, but it does not exert these forces on solute molecules. Clearly, this ideal situation can never be realized completely [3151. For all these reasons, it will be understandable that LLC systems have been virtually replaced by chemically bonded phases (section 3.2.2) in current LC practice. Consequently, the various parameters of interest for the optimization of these systems will not be discussed extensively. With regard to the influence of temperature and mobile phase composition on retention and selectivity, it is suggested that the same relationships may be used for “insoluble” LLC stationary phases as are used for LBPC. LLC systems have been used extensively for the separation of ionic compounds by means of ion-pairing techniques. Such systems will be discussed in section 3.3.2. The main parameters in LLC are the polarities of the mobile and the stationary phase. Increasing the polarity difference between the phases enhances both the selectivity of the system (figure 3.7) and the stability, due to a reduced mutual solubility of the phases. In LLC systems there is not a substantial difference between the selectivity characteristics in the normal phase and the reversed phase mode. The choice of either will mainly be determined by the sample. Polar samples (in polar solvents) will preferably be injected in a reversed phase system and non-polar samples in a normal phase system. Within the framework of the given polarity of a phase, its composition may still be varied for optimization purposes (see the discussion about iso-eluotropic mixtures in section 3.2.2). However, the mutual solubility of the two phases is not only determined by their polarity, so that changes need to be considered carefully. In conventional LLC systems, changes to the stationary phase are hard to make, because they may require a lengthy “re-coating’’ procedure. Dynamic LLC systems

A promising way to create LLC systems with sufficient stability is the use of immiscible ternary mixtures to create what is called a “dynamic” (or “solvent-generated”) LLC system. The principle of such a phase system is illustrated in figure 3.9. This figure shows an example of a thermodynamic phase diagram of a mixture of three components (A, B and C). Both the binary mixtures A + B and A + C are miscible in all proportions. 53

However, this is not the case for solvents B and C and therefore there is a range of binary and ternary compositions at the bottom of figure 3.9 where two liquid phases are formed. If the three solvents are brought together in proportions that correspond to a composition that is situated inside this area, such as the point indicated by a dot in figure 3.9, then two liquid phases will be formed according to the “nodal” line through this point. The position of the point on the nodal line will determine the ratio of the amounts of the two immiscible phases formed. The two liquids thus formed are immiscible, but in thermodynamic equilibrium. Therefore, we may speak of a dynamic system of two immiscible phases. Figure 3.10 shows an example of a practical system applied to create a dynamic LLC phase system. A practical phase system can be created by pumping a mobile phase through a column, the composition of which corrresponds to a ternary mixture that is in dynamic equilibrium with another mixture (the two mixtures can be connected by a nodal line). If the mobile phase is the more polar one of the two ternary mixtures in equilibrium, then a non-polar (hydrophobic) solid support must be used and a reversed phase system can be generated. If the mobile phase is the less polar of the two mixtures in equilibrium, a polar support is required. The phase ratio of the system will largely be determined by the specific surface area of the solid support. Because of the equilibrium between the two phases, dynamic LLC systems are considerably more stable than the conventional LLC systems. If the equilibrium is disturbed by the injection of a sample, then it will soon be restored once the sample starts to move along the column. LLC systems offer a great flexibilitywith regards to the choice of phasesystems. We have seen above (figure 3.8) that the choice of available mobile and stationary phases A

Figure 3.9 : Schematic phase diagram for a ternary system of three liquids, two of which are not miscible in all proportions. A mixture that corresponds to the composition M in the figure will “demix” according to the nodal line LN. Two liquid phases are formed that correspond to the compositions of L and N in the ratio kn.

Figure 3.10 Example of a phase diagram for a ternary system used to create a dynamic LLC system. Components: Ethanol (EtOH), Acetonitrile (ACN) and Iso-octane (2,2,4-trimethylpentane; TMP). I - V nodal lines. Circles: compositiods determined experimentally by titration (full circles) and GC (open circles). Figure taken from ref. [315].Reprinted with permission.

determines the possible (general) selectivity that can be achieved in an L C system. Potentially, LLC systems allow us to use the entire range of the triangle ATW in figure 3.8. This is neither true for RPLC systems (section 3.2.2), nor for LSC systems (section 3.2.3). The possibility to form a truly homogeneous, highly polar stationary phase is a real advantage of LLC systems. Other advantages of LLC systems include the possibility to form reproducible, homogeneous stationary phases, a large sample capacity and a large “contamination capacity” (i.e. LLC columns are not easily polluted by contaminants in the mobile phase or the samples) [315]. Because the LLC system is generally well-defined, it allows a more rigorous theoretical treatment than other forms of LC. In particular, LLC retention data correlate well with liquid-liquid partition coefficients obtained from independent (“static”) experiments. A disadvantage of LLC systems relative to other forms of liquid chromatography (LSC, LBPC) is the long time it takes to create a phase. For dynamic LLC systems, every new mobile phase necessarily requires the creation of a different stationary phase. This may require 50 to 170 (depending on the pore size of the support) times the volume of the mobile phase in the column to be pumped through the system [315]. The phase diagrams of figures 3.9 and 3.10 will be affected considerably by a change in temperature. Therefore, the temperature should be controlled very carefully, as indeed is necessary for all LLC systems. Summary 1. LLC systems are generally not very stable and not very easy to use in practice. 2. The use of dynamic LLC systems may help to overcome some of these problems. 3. LLCsystems ofler a great degree offrexibility with regard to the possible choice of mobile and stationary phases. 4. Well-defined LLC phase systems can be made reproducibly.

5. LLC systems offer high sample capacities and contamination capacities. 6. Temperature is a critical factor for both the stability and the selectivity of LLC systems. 7. Every change in the mobile or stationary phase requires a long equilibration time. 3.2.2 Liquid bonded phase chromatography

3.2.2.1 Reversed phase chromatography ( RPLC) RPLC is currently by far the most popular of all LC techniques [316]. Two reasons for that have already been identified when we discussed LC in terms of solubility parameters. First, a single RPLC column offers great flexibility for the chromatography of a wide variety of solutes by using mixtures of water and an organic solvent as the mobile phase (figure 3.7). Second, the overall selectivity of the RPLC system is almost always superior to that of other LC systems (figure 3.8). Also, in the previous section, some practical disadvantages were described for LLC systems, which have resulted in the almost exclusive use of bonded phases for RPLC. The advantages and disadvantages of RPLC will be summarized at the end of this section. It suffices here to point out that the emphasis put on RPLC in this long section is amply warranted, from a theoretical as well as from a practical point of view. Even more than in other LC techniques, the exact mechanism of retentionin RPLC is unclear. Certainly, a simple picture that would enable us to derive unambiguous equations for the variation of retention with the various parameters of interest cannot yet be drawn. Unfortunately, there has been too much speculation in the literature throughout the last decade, often accompanied with insufficient experimental data to justify the conlusions drawn. Therefore, it is not surprising that there are many different propositions for expressions to describe the retention behaviour in RPLC. In the following pages we will discuss the parameters which are relevant for selectivity optimization and some possible quantitative relationships. The stationary phase Almost exclusively,chemically bonded phases (CBPs) are now being used in RPLC, the vast majority of the applications being achieved on silica-basedphases, modified with long CH3

I I

r-----1

i-OtH

L-----J

CltSi-R

CH3 r------l

-0fH

+ Râ&#x20AC;&#x2122;OtSi-R

L------J

CH3

Figure 3.1 1: Schematic illustration of the reaction of a silica surface with a monofunctional reagent (dimethyl-alkyl-ethoxysilane).Figure taken from ref. 1317). Reprinted with permission.

R EtO -Si

-OEt

HO-&

--OH

a /I\

/I\

/R Si / \

OH\

\ / Si

7 9 Si

/I\

OEt

0 I

0 \

/I\

0 /

Figure 3.12: Schematic illustration of the possible products formed by the reaction of a silica surface with a trifunctional reagent (alkyltriethoxysilane).

alkyl chains [316]. Typically, the silica surface, featuring reactive silanol (-SOH) groups is brought to react with reactive chloro- or alkoxysilanes according to the reaction shown in figure 3.1 1. In figure 3.1 1 a mono-ethoxysilane is used as an example. Alternatively, a trifunctional reagent such as a triethoxy-alkylsilane may be used, to yield what is commonly referred to as a â&#x20AC;&#x153;polymericâ&#x20AC;? material. The various possible products from the reaction of trifunctional silane molecules with the silica surface are shown in figure 3.12. The term polymeric phases arises from the fact that trifunctional reagents may just as well react with each other as with the silica surface under the influence of (inevitably present) traces of water. Hence, the resulting material is not necessarily a well-defined monomolecular layer. Moreover, for every silanol group that disappears during the reaction, two new ones are potentially formed once the product is brought in contact with water. Many of these newly formed silanol groups can subsequently be removed by reaction with a small monofunctional silane (e.g. trimethylchlorosilane, TMCS)*. Also,

* This so-called end-cappingprocess is common practice in the synthesisof bonded phases for RPLC, whether mono- or trifunctional reagents are used. This is done in order to keep the number of remaining silanols to a minimum. 57

many hydroxyl groups can be removed by a heat treatment of the product, because different ligands attached to the silica surface will be “cross-linked” at elevated temperatures. However, a number of the silanol groups will definitely remain present. The presence of these remaining (“residual”) silanols is unwanted, because they may contribute to the retention process, yielding mixed retention mechanisms and increased band-broadening. Because the silica surface is effectively shielded by the hydrophobic layer of long chain silanes, the silanol groups will only exert their influence on solute molecules by long range (electrostatic) interactions. Hence, the presence of silanol groups will be felt more easily at higher pH values (pH > 5 ) where the silanol groups become increasingly negatively charged, and for basic solutes, which may be positively charged at these pH values. Polyelectrolytemolecules (see below) also tend to be affected by the charge of the surface, as they are large enough to experiencethe electrostatic forces of a number of ionized silanol groups. The resulting CBPs are usually identified by the length of the alkyl chain. For example, when the number of carbon atoms in the alkyl chain (nJ is equal to 18, by far the most popular chain length [318], we speak of an octadecylsilica (ODS) or of an RP-18 phase. The second most popular chain length [318] is the octylsilica or RP-8 (nc= 8). Apart from the characteristics of the starting material (specificsurface area, pore sizedistribution) and the reagent used, the alkyl chain length is the only variable to be considered. Upon increasing the alkyl chain length, the retention (k) will initially increase exponentially, i.e. In k increases linearly with nc *. However, when the chain length is increased further, the increase in retention diminishes and the capacity factor becomes roughly independent of the chain length. This is illustrated in figure 3.13. The “breaking point” in the In k vs. nc curves was defined by Berendsen and de Galan [319] as the critical chain length (nz). nr appears to vary with the solute. Tentatively, it increases with the size of the solute molecules. The initial increase of In k with nc is usually larger for solutes for which the absolute retention is larger. Hence, in a plot of In k vs. nc the lines tend to diverge towards larger nr As a rule, therefore, the relative retention (a) increases with nc until the critical chain length is reached (for both solutes). Above this point a will become roughly constant. Although there are exceptions to this rule [319], it does imply that almost always the best selectivity is obtained with n,values above the critical chain length. This is usually realized with ODS phases, which is the largest chain length that is commercially available**. As a conclusion, ODS materials are understandably the most widely applied RPLC stationary phases, and the stationary phase chain length is a variable that will usually not be of interest as a single variable for the optimization of selectivity.

* Note that this observation is in conflict with both a liquid-liquid-likebehaviour of the hydrocarbonaceous layer (in which case k is expected to increase linearly with nJ, and with adsorption of the solute on top of this layer (in which case k would be virtually independent of nJ. ** Even larger alkyl chain lengths have been used to synthesize CBPs, but they would definitely be more expensive if turned into commercial products. Since the critical chain length is usually well below 18 [319], such expensive materials would not usually have major advantages over the existing ODS materials. 58

tj o t

--.-----.--____ rn-cresol -.

01-' 1

,I 6

2-2

Figure 3.13: Variation of the capacity factor with the length of chemically bonded alkyl chains of the stationary phase using monomeric phases (nJ. Mobile phase: methanol-water (8020). Solutes: n-alcohols and aromatic solutes as indicated in the figure. Asterisks indicate the critical chain length. Figure taken from ref. [319]. Reprinted with permission.

The mobile phase In the previous discussion the possibility to use mixtures as the mobile phase has already been mentioned. It was tacitly assumed that a mixture of (for example) methanol and water has a polarity in between those of the two pure constituents. This will generally be the case*. The extent to which retention in RPLC can be made to vary with the composition of the mobile phase is enormous. For almost all solutes retention will be impractically low in some pure organic solvent (methanol, THF) and impractically high in pure water. Hence, to achieve reasonable retention times, a mixture of water and an organic solvent (a so-called modifier) is usually required. We have seen before (section 3.2) how this can be explained in terms of solubility parameters, and it was also concluded that RPLC offers superior selectivity f o r a great variety of samples. First of all, let us recall the basic equation for LC retention in terms of solubility parameters:

In ki = ( v / R T ) { (6,

+ 6, - 26,)(S,

- 6,)}

+ In (n,/nJ.

(3.29)

* Exceptions to this rule will only be observed when two compounds are mixed that exhibit very strong mutual interactions, for example two compounds that give a chemical reaction, or an acid and a base. 59

To a first approximation, we can write for the solubility parameter of a mixed mobile phase 13201

I: (Pi i

(3.34)

where (P is the volume fraction and the subscript j denotes the individual components of the mixture. For a binary mixture of water (W) and an organic modifier ( a )eqn.(3.34) reads

and because the sum of the volume fractions must equal one

,, the volume fraction of the organic modifier. If we combine eqns.(3.29) and where cp= cp (3.36) we find

In ki = (vi/RT) { 6, + ( ~ ( 6 , - 6 ~ )+ 6, - 2Si} { 6, + cp(6,-6,) = (vi/RTr) { (p2(6,- 6,)' + 2 ( ~ ( 6 ,- 6,) (6, - Si) + (6, + 6, - 26,)(6, - as)} + ln(n,/n,).

- a,} + ln(n,/n,) (3.37)

Clearly, eqm(3.37) is a quadratic equation of the form lnk=Aq?+Bcp+C

(3.38)

in which the coefficient A is expected to be positive (see eqn.3.37), B large and negative (because 6, > 6, and 6, B SJ, and Cis the natural logarithm of the capacity factor in pure water. Eqn.(3.38), as well as the expectations for the sign and magnitudes of the coefficients as expressed above, is obeyed very well in practice [321,322]. Only for mobile phase compositions close to (P=O (mobile phases with 10% or less organic modifier in water) may considerable deviations be observed [323]. Hence, eqm(3.38) can be used for the description of the retention as a function of the (binary) mobile phase composition, but the coefficient Cdoes not necessarily give an accurate estimate for the retention in pure water [323]. A similar quadratic equation can be used to describe retention in a ternary eluent, where water is mixed with two organic modifiers, the volume fractions of which are denoted by (P, and (p2 [324]: In k = A,

(P;

4 + Bl

(P1

+ B2

(P2

(Pl(P2

(3.39)

and for quarternary mixtures the obvious expansion would be: In k = A , +

+ A,

(P,~

+ B,

(P1

P (:

+ B,

+ A, (P2

( P ~ ~

+ B3 (P3 +

D13 (P1 (P3 + D23 (P2 9 3

c + D12 (P1 (Pz

(3.40)

The same quadratic equations for retention as a function of composition have been 60

derived by Jandera et al. [325] in other terms (“interaction indices” rather than solubility parameters) but in a very similar way. Melander and Horvath [326] arrive at an equation which is quadratic, but they try to describe their results by a linear relationship between In k and p. Weijland et al. [327]use equivalent quadratic expressions without an underlying model. Their equations are less practical, because the necessary condition that the sum of all volume fractions equals one is not implicitly contained in the expressions, so that a set of two equations remains. They also allow a third order term to allow deviations from the quadratic model. Although the quadratic equations for retention (In k) as a function of mobile phase composition (rp) provide a good description of experimental data, they are inadequate to describe retention within experimental error. For binary mixtures the standard’deviation between the quadratic equation (eqn.3.38) and experimental data is typically between 5 and 10% (depending on the solute) [322]. For ternary systems average deviations of 10 to 20% are typical [324]. However, the inclusion of additional (higher order) terms at will is not an attractive way to improve the description of the experimental data. We will discuss this more fully in chapter 5 (section 5.5). Alternative expressions Several other equations have been suggested for RPLC. Purnell et al. [328] suggested plotting 1/ k vs. rp. A straight line in such a plot would correspond to the same assumptions as were used to explain the validity of eqn.(3.14) in GLC. However, straight lines are not observed, but instead plots of l / k vs. pshow a pronounced curvature towards the (paxis. Purnell et al. [328] proceeded to describe l / k as a function of p using the following four-parameter hyperbolic equation: (3.41) This equation may be used not only for RPLC, but also for other forms of liquid chromatography. Melander and Horvath [329] have suggested a five-parameter hyperbolic equation to describe k itself as a function of rp: A ~ ~ +r p +c (3-42) k= A’ cp+ B‘ Eqn. (3.42) is an example of a so-called “rational function”. Functions of this kind are renowned for their flexibility in describing curves without physical modelling. Lu Peichang and Lu Xiaoming derived a three-parameter parameter equation, which reads [3301

Ink=a+ Bp+clnq.

(3.43)

Obviously, eqn.(3.43) will not be able to yield a successful description of the retention behaviour in the range of low rp values. Therefore, it was subsequently modified to Ink = a

+ cln(1 + d q ) .

(3.44) 61

None of the equations (3.41) to (3.44) appears to offer a better compromise between the accuracy of the description and the complexity of the model than does the quadratic equation (3.38). Linear approximation for binary mixtures

The quadratic expressions facilitate the description of retention over large ranges of composition. Such large ranges are usually of limited interest. Both very small (insufficient resolution) and very large (excessiveretention times) capacity factors are unattractive. The most useful range of capacity factors is between 1 and 10 (cf. sections 1.5 and 1.6). Over this limited range eqn. (3.38) for a binary mixture can usually be approximated quite adequately by a straight line [322,331]: I n k = In ko - S q ,

(3.45)

where k, is an imaginary (extrapolated) capacity factor in pure water*. Although a part of the curve for binary mixtures can be approximated by a straight line, this does not imply that a part of the retention surface in ternary mixtures can be approximated by a plane. Straight line approximations can only be used for quasi-binary mixtures, i.e. ternary mixtures in which the ratio of the volume fractions of the two organic modifiers is constant. Two of such straight lines (for different ratios) do not usually define a plane. Initially, Snyder [331] suggested that the slope S in eqn.(3.45) would be independent of the solute, i.e. S would be a constant for a given stationary phase and two given mobile phase constituents. For example, for methanol-water mixtures on an ODS column S was claimed to be about 7 [331]**. Hence, eqn.(3.45) would be approximately valid over a composition span of 30%( = 2.3 x l O O / S ;there is a span of 2.3 units in In k between k = 1 and k = 10). Since then, however, it has been shown that the value of S does vary systematically with the retention behaviour of the solute [322,333]. If binary mixtures of water and methanol are used as the mobile phase, S tends to increase with an increase in the absolute retention. This is illustrated by the diverging set of lines in figure 3.14***. In the methanol-water system, a linear correlation between the coefficients S and In ko has been observed by several researchers [322,333], and the coefficients p and q describing this linear relationship as S = p + qlnk,

(3.46)

* What is true for the coefficient C in eqm(3.38) is certainly not less true for In k, in eq~(3.45).Both coefficients cannot be relied upon to provide accurate estimates of the (logarithmic) capacity factor in pure water [323,332]. ** Snyder used decimal logarithms instead of natural ones, causing a difference of a factor of 2.3 between the value given here and the literature data [331]. *** Note that the simple solubility parameter model (eqn. 3.37) predicts the coefficient B to be dependent on the (polarity of the) solute and, moreover, predicts the magnitude of B to increase if the solute polarity decreases. For RPLC this implies an increase of the slope with an increase of the retention. 62

water

methanol

'T Figure 3.14: Variation of retention with the binary mobile phase composition for methanol-water mixtures on an ODS column. Solutes: naphthalene ( ), anisole (0)and phenol (x). Thin lines: eqn. (3.38) for k < 50; thick lines: eqn.(3.45) for 1 < k < 10. The diverging straight lines suggest an increase of the slope parameter S (eqn.3.45) with increasing capacity factors Figure taken from ref. [322]. Reprinted with permission.

have been estimated with remarkable consistency, despite the use of different solutes and different columns for the evaluation. The parameters found for the coefficients in eqn.(3.46) are summarized in table 3.1. An example showing the validity of eqn(3.46) for 32 aromatic solutes is given in figure 3.15. Although some justifiable comments can be made regarding the use of linear regression techniques on logarithmic equations [334],the correlation described by eqm(3.46)certainly appears to be significant, and it may be used in an elegant way to reduce the parameter space for the optimization of RPLC separations (section 5.4.2). Eqm(3.46) thus appears to hold reasonably well for the methanol-water system. However, it is obeyed much less strictly in the system tetrahydrofuran-water and not at all in the system ACN-water. There appears to be no sensible explanation yet for these anomalies. Data observed on the correlation between In k, and S for these two binary mixtures are also included in table 3.1.

The concept of iso-eluotropic mobile phases As we saw above (eqn.3.34), the solubility parameter concept provides a very simple rule for approximating the polarity of a mixture. For a binary mobile phase containing water (W) and methanol (Me) the sum of the two volume fractions should equal 1, hence

(3.47) is a very simple equation for the polarity of such a mixture. According to eqn.(3.47), a given mixture of methanol and water will have a given polarity somewhere in between the polarity of pure methanol and that of pure water. Of course, the same solubility parameter 63

may be obtained with several other mixtures. In general, a mixture of a given polarity may be formed by mixing two solvents, one with a higher polarity than the required value and the other with a lower polarity.

I 10 -

. 5=2.27+079Ink, corr coeff. :0.98 5-

/* ~

Ink,

Figure 3.15: Variation of the slope with the intercept for linear retention vs. composition curves in RPLC for 32 aromatic solutes on an ODS column using methanol water mixtures as the mobile phase. Parameters S and In k, correspond to eqn. (3.45). Figure taken from ref. [322]. Reprinted with permission.

Table 3.1: Parameters describing the linear relationship between the slope and the intercept of linear retention vs. composition curves in RPLC (eqn.3.46). Data taken from refs. [322] and [333] (1). Stationary phase

Modifier

r (2)

Lichrosorb RP-18 Hypersil ODS Hypersil ODS Nucleosil 10-RPI8 Nucleosil 10-RP18 Lichrosorb RP-18

MeOH MeOH MeOH MeOH MeOH MeOH

2.27 3.73 3.62 3.55 2.97 3.50

0.79 0.74 0.79 0.69 0.75 0.73

0.98 0.96 0.96 0.94 0.93 0.98

Lichrosorb RP-18

ACN

5.87 (3)

Lichrosorb RP-18

THF

4.33

0.78

- 0.06

0.76

(1) Data in ref. [333]are acompilation from other sources. The values for the intercept were multiplied by a factor of 2.3 (In 10) to account for the use of natural logarithms in the present text. (2) Correlation coefficient. (3) Average S value, since no correlation was observed.

To a first approximation (eqn.3.29) we may expect mixtures of the same polarity to yield the same capacity factors. In other words, mixtures with the same solubility parameters are expected to have the same eluotropic strength, and therefore they might be called iso-eluotropic mixtures. If we use T H F (T) instead of methanol in a binary mixture with water, the following equation relates two iso-eluotropic mixtures (3.48) where cpr is the volume fraction of THF. From this equation it follows that 'Me

-W '

(3.49) 'PMe ' ST-', If we use 15.85 for the solubility parameter of methanol, 25.52 for water and 9.88 for T H F (see table 2.2), we find that

cpr=

Hence, a mixture of 50% methanol in water is expected to yield roughly the same capacity factors as a mixture of 31% T H F in water. Similarly, for acetonitrile with a solubility parameter of 13.14, we find that (3.51) These very simple relationships can be verified experimentally as is shown in figure 3.1 6. The iso-eluotropic compositions of binary mixtures of T H F and acetonitrile with water have been plotted against the binary methanol-water composition. The thin straight lines indicate the theoretical relationships from solubility parameter theory (eqns. 3.50 and 3.51). The thick lines correspond to average experimental data over large numbers of solutes [335]. An (average) experimental data point can be found as follows. For a particular solute, a capacity factor of 3 may be found in a 50150 mixture of methanol and water. For the same solute, a mixture of 34 %THF in water may also yield a capacity factor of 3. For a different solute, the capacity factor in a 50150 methanol/water mixture may be 30, and the same capacity factor may be observed with a 28/72 THF/water mixture. The average composition for many solutes that yield the same capacity factor as the 50/50 methanoVwater mixture yields the (average) experimental point on the solid line for T H F at cp = 0.5 in figure 3.16. Due to specific effects, the corresponding compositions of methanol and T H F will not be exactly the same for all solutes. Conversely, when the iso-eluotropic composition is taken as the average of that observed for many solutes (or from solubility parameter theory), some solutes will be eluted later than with the original methanol/water mixture, and some will be eluted earlier. The relative differences may amount to a factor of two for certain solutes. This should not be seen as an error in establishing iso-eluotropic mixtures. Rather, it enables us to exploit iso-eluotropic mixtures to enhance selectivity, whilst keeping retention roughly constant. This principle is widely used for the optimization of selectivity in LC. Figure 3.1 6 shows that there is good agreement between (solubility parameter) theory 65

and experiment for the composition of iso-eluotropic mixtures in RPLC. The great advantage of this is that the composition of iso-eluotropic mixtures may be predicted for other organic modifiers than THF and acetonitrile. In table 3.2 a selection of practically feasible RPLC modifiers is given [336]. The table lists their solubility parameters and their selectivity group classification according to Snyder (see section 2.3.3). Solvents within a given group show very similar selectivities in gas chromatography (see table 2.8). Therefore, it may be expected that the specific effects observed in LC will also be similar for modifiers in the same group. For each modifier, the percentage that is equivalent to one percent of methanol in binary mixtures with water (A,) is listed in the table. Extension to multicomponent mixtures We can easily extend the above treatment to iso-eluotropic mixtures that contain more than one modifier. Let us rewrite eqn.(3.51) in a simplified form (3.52) which relates the volume fraction of a modifier j in a binary mixture with water to the volume fraction of methanol in a binary reference mixture ( ( P ~ ~ A, , ~denotes ~ ~ ) .the ratio of solubility parameter differences: (3.53) According to the simple solubility parameter model any mixture of two iso-eluotropic mixtures (same value for s) would yield a mixture that is iso-eluotropic to the original two (eqn.3.34). It then follows from eqa(3.52) that for any ternary mixture of two iso-eluotropic binaries the following equation holds

I' I

Figure 3.16: Iso-eluotropic compositions for binary mixtures of THF and acetonitrile in water, relative to methanoVwatermixtures. The solid lines represent the average experimentalcompositions for a large number of solutes. The thin lines represent calculated compositions from solubility parameter theory (eqns.3.50 and 3.51). Figure taken from ref. [311]. Reprinted with permission.

pMe,ref

P M e -k Pj’’j

(3.54)

which can be expanded to multicomponent mixtures formed by blending a series of iso-eluotropic binary mixtures (3.55) It follows from eqn.(3.54) that iso-eluotropic ternary mixtures fall on a straight line in a figure where the two variables pMeand pj constitute the axes. Iso-eluotropic quarternary mixtures constitute a.plane in a three-dimensional space, and so on. Eqm(3.54) and (3.55) are very convenient for the definition of iso-eluotropic mixtures and for the calculation of the eluotropic strength of multicomponent mobile phases, in terms of a corresponding binary methanol/water mixture. The solubility parameter model appears to work very well for the prediction of iso-eluotropic mixtures in LLC and RPLC. However, in LSC the retention mechanism is very different from the one that was assumed at the outset of this section, and hence a different model should be applied to allow the description and possibly prediction of the eluotropic strength in LSC. This model will be described in section 3.2.3. Temperature

Unlike the relationship between retention and composition, the temperature dependence of retention in RPLC is beyond dispute. A typical “van ’t Hoff-type” equation may be used: Table 3.2: Iso-eluotropic mixtures for RPLC. Modifier (in water)

6 (1)

Aj (2)

Selectivity group (3)

(~aI’’*.cm-~’*)

relative to MeOH

Methanol Ethanol n-Propanol i-Propanol

15.85 13.65 12.27 12.37

1 0.81 0.73 0.74

Acetonitrile

13.14

0.78

VIb

Acetone

10.51

0.64

VIa

THF 1,4-Dioxane DMSO

9.88 10.65 13.45

0.62 0.65 0.80

111 111 111

I1 I1 I1

(1) ref. [303] (2) Eqn.(3.53) with Sw=25.52. (3) See section 2.3.3.

In k = A h / R T - A s / R

+ ln(ns/n,,,),

(3.56)

where Ah and As are the (partial molar) enthalpy and entropy effects for the partition of the solute over the two phases, R is the gas constant and Tthe absolute temperature. n,/ nm is a phase ratio term (cf. eqn.3.29). Schematically,the temperature effect may be described by Ink= A / T + B,

(3.57)

where the coefficient A is usually positive, so that retention will decrease when the temperature is increased. The effect of changes in temperature on retention and selectivity is not very large. Certainly, the mobile phase composition (water content) has a much more drastic effect on the retention. However, what was true for GC (cfsection 3.1) is also true for LC. Temperature and composition cannot be seen as independent variables, and a different optimum (mobile phase) composition is likely to be observed at a different temperature (see section 5.1.1). Snyder et al. [337] have demonstrated the combined effects of the composition of a binary mixture and temperature on the retention and selectivity. An increase of the temperature has the predictable effect of a decrease in retention, with little effect on the selectivity. Since there is usually only a small margin for which the retention of all the solutes in a given sample is neither too high nor too low, drastic changes in the temperature in order to enhance the selectivity cannot be applied. However, a decrease in retention due to an increase in the temperature can be compensated by increasing the water content of the mobile phase. In the case in which methanol-water mixtures are used as the mobile phase, this is likely to result in an increase in the selectivity, because of the regular pattern of In k vs. cp lines diverging towards cp=O (cf.figure 3.14). Hence, an increase in the temperature combined with an increase in the water content of the mobile phase will usually result in an increased selectivity, while retention may be kept constant. A disadvantage of the operation of RPLC columns at elevated temperatures may be a more rapid detoriation of the column because the silica is more rapidly dissolved in the mobile phase. This effect may also lead to a reduced reproducibility of the system (peakwiths and capacity factors). A simple but useful equation to express the mutual effects of temperature and mobile phase composition on retention has been described by Melander et al. [338]: I n k = A, cp(1-

TJT)

A,/T

A,,

(3.58)

where A,, A,, and A, are constants for a given solute using a given stationary phase and two given mobile phase components. T, is the so-called compensation temperature*, at which the retention is independent of the mobile phase composition. For all practical

* The term compensation temperature arises from the compensation between enthalpy and entropy at the temperature T, This temperatureturns out to be virtually independent of the solute in an RPLC system [339]. The magnitude of T, (200 - 300 "C) usually implies that it is a hypothetical rather than a practical temperature. 68

purposes T, can be considered as an arbitrary coefficient, the value of which may be determined from experimental retention data. A minimum of four experimental data points is required to estimate the parameters in eqn.(3.58), similar to the experimental design employed by Snyder et ul. [337]. Of course, eqn.(3.58) can only be applied over a limited range of compositions, for example the range over which 1 < k < 10. To describe retention as a function of both temperature and composition over wider ranges of the latter, more complicated equations need to be used. A quadratic equation for the relationship between retention and composition' (eqn.3.38) can be combined with eq~(3.57)to yield I n k = A'(l-u/T)q2+

B'(l-b/T)q+

C'(1-c/T),

(3.59)

where A', B' , C' , u, b and c are all constants. At constant temperature this equation reduces to eqn.(3.38), while at constant composition it turns into eq~(3.57).

The pH of the mobile phase will affect retention in liquid chromatography if the structure of the solute molecules in solution is affected by the pH. This will clearly be the case if the solute species may occur in a protonated or a non-protonated form, dependent on the pH. The pH may also affect the capacity factors of ions and neutral molecules for which this is not the case, but in this case the effects are usually small. Retention in RPLC may be expected to be a strong function of the pH if 1. different forms of the solute (e.g. protonated vs. non-protonated) may exist in the mobile phase, which show different retention times, and 2. the (relative) occurrence of the different forms of the solute changes upon variation of the pH. If two different forms of the solute exist, then the first requirement will usually be met, especially for simple monofunctional solutes. The most obvious example is the dissociation of a weak acid (HA) in an aqueous environment: HA

+ H,O

A-

+ H30+ .

(3.60)

Because HA is a neutral (uncharged) molecule and A - is a negatively charged ion, the retention between the two species of A may be expected to be very different. The second condition depends on the range of pH variation with respect to the equilibrium constant of the solute. The dissociation constant of HA is defined as K, = [A-1 [H,O+l

[HA]

(3.61)

so that for the ratio between the two different species of A ( r A ) rA =

[A-]/[HA] = K,/[H,O+]

(3.62)

Eqn.(3.63) shows that the greatest variation of rA can be expected around pH = pK,, where rA= 1. When the pH exceeds the p K , value by two units, then rA= 100, so that more than 99% of the solute is dissociated. When the pH is two units below pK,, then rA= 0.01 and less than 1% dissociation occurs. Hence, the second condition will be met if the pH is varied in the region of the pK, value of the solute. Since for silica-based RPLC columns the working range is limited to 2 < pH < 7, solutes with 1 <pK,< 8 may be expected to show variations in retention upon changing the pH over the entire range allowed. In other words, for weak acids with a pK, value in the above range the pH is a parameter of interest. A similar argument can be set up for basic solutes. The followingschematic reaction may serve as an example:

+ H,O

e XH+

+ OH-

(3.64)

and a dissociation constant may be defined as

so that rx = [XH+] / [ A= K, / [OH-]

(3.66)

and log rx = log K,

+ log [OH-]

= 14-pH-pKb.

(3.67)

Hence, the greatest variation in rx is observed for pH values around pH = 14- pK, *. On silica-based RPLC columns the range of 2 < p H < 7 will correspond to bases with 7<pK,< 12. For these very weak bases pH is a relevant parameter in RPLC. Much stronger bases @K,< 6) will be protonated completely, or almost completely in RPLC using silica-based CBPs. On these columns, their ionization cannot be suppressed, and they should be chromatographed as ions, either on ion-exchange or on ion-pairing systems (see section 3.3 below). There has been much recent interest in the development of column packings for RPLC that can be used over a wider pH range. Potential materials include organic polymers, carbon packings and (modified) alumina. Clearly, such stationary phases will be most relevant for the separation of basic solutes. If a buffer is present in the mobile phase, then the dissociation will be controlled by the pK, value of the buffer. Because of the pH limitations of silica-based stationary phases, only weak acids can be used as buffer compounds. As an example, we will consider the dissociation of a weak acid (HA) in the presence of a buffer acid (HB).

* In an aqueous environment the p K , and p K , values, which correspond to the same reaction, may ~~

be related by p K , + p K , = 1 4 .

The following equation can readily be derived [340]: rA

[A -1

HA1

- [A-I[H,O+l

[HA1

[HBI [B-I[H,O+l

.-[B-I

[HBI (3.68)

where Ka.Ais the dissociation constant of the solute, K a , Bthe dissociation constant of the buffer, rBthe dissociation ratio of the latter and K , , is a constant. Hence, the dissociation ratio of A is proportional to the dissociation ratio of the buffer. The ratio rB is a more practical quantity than the pH in mobile phases other than pure water [341]. The pH is ill-defined in such mobile phases, but the ratio of the salt and the acid that constitute the buffer in pure water a known quantity. An equation for the observed capacity factor (kobs)can be derived if it is assumed that the acid-base equilibrium kinetics are fast enough to be considered as instantaneous. This corresponds to the observation of a single sharp peak for the ionizable species in the chromatogram. In that case it may be assumed [340,342,343] that for the weak acid HA kobs

kHA

[ HA1

[HA1+ [A -1 +

HA + k 1 + rA

[A-I [HA]+[A-]

(3.69)

or with eqn(3.63) (3.70) Eqm(3.70) is a three-parameter equation which describes the relationship between retention and pH for weak acids. If the dissociation ratio of a buffer ( r B = [B-]/[HB]) is used as a variable instead of pH, then a combination of eqm(3.68) and (3.69) leads to (3.70b) which again is a three-parameter equation. Similar equations can also be derived for weak bases. Figure 3.17 shows the observed capacity factor for a weak acid as a function of the pH. Arbitrary values of k , = 1 (for the solute ion) and k H A= 9 have been assumed. It is clear from the figure that only in the vicinity of the p K , value can a large effect of the pH on retention be observed. If the pH range studied ranges from pH =p K a + 1 upward, then the variation in kobsis less than 1O0/oof the total variation between k , and k H AA . similar minor effect is observed at pH values below p K a - 1. Figure 3.17 shows that complicated sigmoidal curves are obtained for retention as a function of the pH over a range encompassing the pK value of the solute. Simple approximations are not possible in this 71

range. Plotting different transformations of the variables will not simplify the picture*. A practical example of the variation of retention with pH in RPLC can be found in fig.5.17. Three experiments are in principle sufficient to establish the three coefficients in eqn(3.70) for a given solute. In practice this is only true if the three experiments are taken at such values of the pH (relative to p K J that a sensible estimate of all three coefficients can be made. This implies one experiment within one pH unit of the p K , value, one experiment at a higher and one at a lower pH. If the p K , value of a solute is known, then the retention behaviour can be estimated from a minimum of two experiments. Another way to reduce the minimum number of required experiments is to assume a negligible capacity factor for the charged species. Of course, once more experimental data points become available initial assumptions about the value of any of the coefficients in eqn.(3.70) can be abandoned. Multivalent ions

So far we have discussed the behaviour of monoprotic acids and monofunctional bases. The behaviour of bifunctional or trifunctional acids and bases is not completely different.

L, '

pKa -3

, PKO

PKo+3

Figure 3.17: Schematic illustration of the variation of the observed capacity factor (kobs)with the pH for a weak acidic solute in RPLC according to eqn.(3.70). The retention line is calculated from eqn.(3.70) assuming k, = 1 and k H A= 9.

* This may only be done if both k , and k,,, are known, for instance form measuments performed at pH values well above and well below the p K , value. In that case the following transformation of eqn.(3.70) will result in a straight line:

The most important equilibria are those in which one of the two species is ionized, while the other is neutral. In many situations in RPLC both the monovalent and di- (tri-, etc.) valent ions have negligible capacity factors in comparison with the neutral molecule. Therefore, often all but one of the dissociation constants of an oligovalent species can be neglected. Equations for the influence of the pH on the retention of diprotic and oligoprotic substances can be found in ref. [316], p.239 et seq.. More value should be assigned to the possible formation of multivalent ions if separations based on the ionic character of the solute are considered (section 3.3). A special place is taken by polyelectrolytes. These are molecules containing a large number of ionizable groups, each of which can be assumed to behave in a manner similar to a single weak acid or base. However, the combination of a large number of these functionalities gives rise to a total charge of the molecule that varies continuously from a large positive number at a low pH to a large negative number at a high pH. Proteins are good examples of such polyelectrolytes. At some pH, the overall charge of the molecule will be zero. This does not imply that there is no charge on the molecules, but only that the total number of positive charges equals the number of negative charges. This point of zero electric charge is called the isoelectric point, and the pH value at which it occurs is denoted as PI. Polyelectrolytesshow a variation of retention with pH over the entire range. However, it should be noted here that their chromatographic behaviour is complicated. It is not usually possible to isolate different retention mechanisms. In the chromatography of proteins ionic mechanisms, physico-chemical interactions and size exclusion may all play a role [344]. Ionic strength The ionic strength of the eluent will affect the retention of both neutral and ionized species. For non-charged molecules the effects of increasing the ionic strength of the eluent can be understood as an increase in the mobile phase polarity, leading to an increase in retention (â&#x20AC;&#x153;salting-out effectâ&#x20AC;?). For charged species it was shown by van der Venne et al. [345] and by Otto and Wegscheider [346] that the so-called Davies equation can be used to describe the effect of the ionic strength on solute retention quantitatively. This equation reads (3.71) where k, is the capacity factor at zero ionic strength, A a temperature-dependent constant (equal to 0.512 at 25 â&#x20AC;&#x153;C [345]), z the charge of the solute ions and 1 the ionic strength (M). It can be seen from the above equation that the ionic strength will have a similar effect on solutes of similar charge. Only if the charges of the components to be separated are different can the ionic strength be used to vary the chromatographic selectivity. Summary

At the end of this section we may summarize the advantages and disadvanatages of RPLC. The parameters that may be used for the optimization of the selectivity will be summarized in section 3.5.1 (table 3.10~).The major advantages of RPLC are: 73

1. RPLC is a veryflexible chromatographic method. It can be applied to a great variety of

samples (seefigure 3.7). 2. Theoretically, RPLC ofiers a superior selectivityfor all but the very polar samples (see figure 3.8). 3. RPLCcolumns with chemically bonded (alkyl)stationaryphasesprovide rapid equilibration, high eflciency and symmetrical peaks. 4. RPLC is compatible with aqueous samples, but also with a number of organic sample solvents. 5. The aqueous mobile phases used in RPLC allow the use of buffers in the mobile phase. This may lead to improved selectivity and eficiency. Secundary (ionic) equilibria other than acid-base dissociation may also be used (see section 3.3.2). Some disadvantages of RPLC remain. These may be summarized as follows:

1. The current alkyl modified silica stationary phases are not truly non-polar. This leads

to a reduction of the overall selectivity (seefigures 3.7 and 3.8). 2. Residual silanol groups are present on the surface, which may have a negative effect on the peak shape of basic solutes and poly-electrolytes in particular. 3. Current RPLC stationary phases are only stable over a limited range of pH. A reliable working range is 2<pH< 7. 4. The mechanism of RPLC is still poorly understood and reliable quantitative theories are not yet available. It appears from this summary, that most of the disadvantages of RPLC are not fundamental, but connected to the use of a particular kind of stationary phases (alkyl modified silicas). It may therefore be expected that advances in this area will further enhance the potential of RPLC. 3.2.2.2 Polar bonded phases Besides the typical RPLC stationary phases with n-alkyl groups, various other functional groups may be chemically bonded to the surface in a similar way as described in section 3.2.2.1. A selection of possible bonded bases, arranged roughly in order of increasing polarity, is given in table 3.3. Apart from the perfluorinated phases, the polarities of the CBPs in table 3.3 are typically intermediate between those of the non-polar alkyl phases and polar adsorbents such as silica. As we saw in figure 3.8, such phases may be operated with a polar eluent in the Reversed Phase mode, or with a non-polar (or weakly polar) eluent in the Normal Phase mode. The elution order of the sample components will be reversed in these two cases. A clear example of this phenomenon has been described by Kirkland [347] for the separation of some urea herbicides using a CBP with aliphatic ether groups. We also saw in figure 3.8 that moderately polar stationary phases may be most useful in the reversed phase mode for the separation of very polar solutes, which cannot be sufficiently retained on reversed phase (alkyl) materials. A good example of this is the separation of carbohydrates on amino bonded phases. Chemically bonded phases may also be tailored to a specific separation problem. A case in point is the synthesis of chiral stationary phases for the separation of optical isomers. Another application of polar bonded phases, which is beyond the scope of this book, 74

Table 3.3: A selection of chemically bonded phases featuring different functional groups. Type

Functional group

RP-F (Perfluorinated)

- CnF*n+l

RP-n (n-alkyl)

- CnH2n + 1

Phenyl

TP -0

Cyano

- C = N

Diol

Amino

- NH2

Cyclohexyl

- CEL

is to be found in size exclusion chromatography, where the chemical modification is aimed at minimizing rather than enhancing specific interaction between the solutes and the stationary phase. In principle, the composition of the stationary phase may be varied by using â&#x20AC;&#x153;mixed phasesâ&#x20AC;?. Phases which incorporate different functional groups in a given ratio have been synthesized (see for example ref. [348]). However, retention may not be expected to vary linearly with the composition of such mixed phases in a manner similar to what is observed with mixed liquid phases in GLC (section 3.1.1). This, combined with the complications involved in preparing mixed phases and the irreversibility of bonding reactions, excludes the composition of mixed CBPs as a practical parameter for optimization purposes. The stability of polar bonded phases is generally considered to be less than that of n-alkyl phases, because the Si-0-Si-C bonds are less effectively shielded against nucleophilic attacks (ref. [316], p.125). The mechanism of separation on polar bonded phases is not clear. Due to their limited proliferation, no theories have been developed solely to descibe this particular form of liquid chromatography. Instead, descriptions from other fields may be applied. If polar bonded phases are used in combination with more polar mobile phases in the reversed phase mode, then the same rules may be applied as in RPLC (section 3.2.2.1) to describe the effects of the mobile phase, the temperature, the pH, etc.. When used with less polar mobile phases in the normal phase mode, LBPC may be treated similarly to LSC (section 3.2.3). The same solvents may be recommended for use in these two forms of LC (ref. [349], p.284). However, the use of particular bonded phases may impose some constraints on the choice of solvents. For instance, amino type columns would be modified (reversibly) by mobile phases containing acetic acid and (irreversibly) by acetone. 75

3.2.3 Liquid-solid chromatography (LSC) In liquid-solid chromatography (LSC) the solute is distributed between a liquid mobile phase and a solid surface. A distribution coefficient may be defined in an analogous way as in GSC (eqn.3.16): ‘a,,

<,s/Ci,m

(3.16)

where Ka,,is the adsorption coefficient (ml/g), c:,~the concentration of the solute on the stationary phase (mole/g) and c, as usual, the concentration in the mobile phase (mole/ml). In principle, the adsorption isotherm is non-linear, i.e. K,., varies with varying c , , ~Only . at very low concentrations may an approximately linear distribution isotherm be assumed. Therefore, LSC techniques suffer from a low sample capacity. Snyder [350] has given an early description and interpretation of the behaviour of LSC systems. He explained retention on the basis of the so-called “competition model”. In this model it is assumed that the solid surface is covered with mobile phase molecules and that solute molecules will have to compete with the molecules in this adsorbed layer to (temporarily) occupy an adsorption site. Solvents which show a strong adsorption to the surface are hard to displace and hence are “strong solvents”, which give rise to low retention times. On the other hand, solvents that show weak interactions with the stationary surface can easily be replaced and act as “weak solvents”. Clearly, it is the difference between the affinity of the mobile phase and that of the solute for the stationary phase that determines retention in LSC according to the competition model. Snyder [350]formulated the following equation to describe the above effect quantitatively: log K,., = log V,

a (Sp - A , 8).

(3.72)

In this equation is the adsorption energy of the solute on a standard adsorbent. A, is the adsorption area of the solute molecule. 8 is the adsorption energy of the solvent per unit area on the same standard adsorbent*, usually referred to as the solvent strength or eluotropic strength. a i s the activity of the adsorbent and V , is the volume of the adsorbed solvent per gram of stationary phase. Hence, V, can be seen as a compensation factor for the dimensions of K,.,.K a / V , is a dimensionless quantity. The choice of units and standards for the remaining variables is arbitrary. The following conventions were followed by Snyder [350]: standard adsorbent (a=1) : dry alumina standard solvent (8= 0) : n-pentane standard solute area (A,=6) : benzene**

* 8 is the solvent adsorption energy (S$ equivalent to for the solute) divided by the adsorption area of the solvent (As). Hence, the competition factor can be rewritten as sp - A i 8 = / t i ( -

g --) -q

This expression shows more clearly that the competition is based on the adsorption energy per unit area, i.e. e / A , vs. e / A r ** This convention for A, implies that one unit in A, corresponds to approximately 8.5 A*.

Using these conventions, values for a (different adsorbents), 8 (different solvents), and A i (different solutes) can be established from chromatographic experiments (for procedures see ref. [350]). Eqn. (3.72) describes retention in LSC in terms of separate parameters for the adsorbent (V,, a), the solute A i ) and the solvent (8). As such, it has proved invaluable for the interpretation of retention and selectivity phenomena in LSC. For example, the effect of a change in the solvent using the same stationary phase and the same solute can easily be understood in terms of a variation in EO. Unfortunately, this is no longer true once several parameters are changed at the same time. For instance, the value of 8 appears to depend not only on the solvent, but also on the adsorbent. Hence, different 8 values have been tabulated for different adsorbents. Some examples of values for common solvents are collected in table 3.4. Clearly, the values for 8 are different on silica and alumina. They are very different from those observed on carbon, which is partly, but not entirely due to the different conventions used in this case by Colin et al. 1351). Likewise, the solute parameters A i and will be different for different adsorbents. Hence, eqn.(3.72) gives a consistent description for one particular stationary phase. A new set of parameters will have to be established for each new adsorbent. As a consequence, the influence of the stationary phase on retention and selectivity cannot be explained on the basis of eqn.(3.72).

(9,

Influence of the mobile phase The influence of the solvent in LSC is described by the solvent strength parameter 8. Table 3.4 Eluotropicstrength [349] en [351].

(Eâ&#x20AC;&#x2122;,

eqn.3.72) of some common solvents for LSC. Data taken from refs.

Solvent Alkanes 1Chlorobutane Chloroform Methylene chloride Isopropylether Ethyl acetate THF Acetonitrile Methanol

silica

alumina carbon

0.01 0.20 0.26 0.32

0.01 0.26 0.40 0.42 0.28 0.58 0.57 0.65 0.95

0.34

0.38 0.44 0.50 0.7

0.10-0.17 0.13 0.18 0.13

0.13 0.14 0.04 0 (3)

(1) 7 8.42 9.87 10.68 7.60 9.57 9.88 13.14 15.85

Select. group (2)

V Vlll V I VI I11 VI I1

(1) Solubility parameter in ca1â&#x20AC;?2.cm-3â&#x20AC;&#x2122;2 [303].

(2) See section 2.3.3. (3) By definition, see ref. [351].

According to eqn.(3.72) a higher value of 8 will result in a lower value for the capacity factor. It can be concluded from table 3.4 that the solvent strength on silica and alumina stationary phases roughly increases with increasing polarity (6)of the solvent, but that there is no quantitative correlation between these two solvent properties. For example, ethers are much stronger solvents (especially on silica) than can be anticipated on the basis of their solubility parameters. Although the number of pure solvents that is compatible with the LSC system is much larger than it is for RPLC (section 3.2.2.1), mixtures are frequently employed as mobile phases. Snyder [350] has developed the following equation for the dependence of the solvent strength (8) on the composition (N, the mole fraction of the stronger solvent B) in a binary mixture

G B=

+ (l/an&log

{ N b 10

anb(G- 4) + 1 -

Nb}

(3.73)

where n b is the molecular size of the solvent B and a is again the activity of the stationary phase. Figure 3.18 shows the variation of G Bwith the composition for a series of binary mixtures in which n-pentane is the weaker of the two solvents. The experimental points in the figure show that at least for these mixtures eqn.(3.73) provides a good quantitative description. According to eqn.(3.72)log (1 / K,,J is proportional to G Band the same is true for log (l/k). Therefore, the variation of retention with composition in LSC appears to be rather complicated.

LO 60 % Blvlv)

100

(GB)

Figure 3.18: Variation of the eluotropic strength with the composition of the mobile phase in LSC (eqn.3.73). Weak solvent is n-pentane; Strong solvents (from bottom): carbon tetrachloride, n-propylchloride,methylenechloride, acetone, pyridine. Figure taken from ref. [349]. Reprinted with permission.

I 2

Figure 3.19: Variation of retention with composition in LSC according to the simplified linear relationship of eqn.(3.74). Stationary phase: Lichrosorb ALOX T (Alumina). Mobile phase: n-propanol (rp is volume fraction) in n-heptane. Solutes: lumisterol (l), tachysterol (2), calciferol (3) and ergosterol (4). Figure taken from ref. [357]. Reprinted with permission. However, a much simpler relationship between retention and composition may often be observed in practice. It was suggested by Soczewinski [352,353] that a plot of In k vs. In X, (where X , is the mole fraction of the stronger solvent B) would yield a straight line, according to

I n k = c - nInX,,

(3.74)

where c and n are both constants. In fact, as pointed out by Jandera and ChuraEek [354], Soczewinski’s eqn.(3.74) is a simplified version of the treatment of Snyder. Figure 3.19 shows an example of the linear variation of retention with composition according to eqm(3.74). In this figure the logarithm of the volume fraction ( q ) of the stronger solvent is plotted on the horizontal axis. Plotting In X , will lead to a similar linear plot. The simple equation of Soczewinski (eqn.3.74) often yields a very good description of experimental data in LSC [353,355,356]. Small percentages of strong solvents (so-called “modulators”) are seen to have a drastic effect on the value of .z0 (see figure 3.18). This is especially true for the most polar solvent of all, water. Therefore, the water content of the mobile phase and the extent to which the

stationary surface is covered with water are critical parameters in LSC. Besides a drastic reduction in the retention time, an improved peak shape may be the result of the addition of water to the mobile phase. Both the column efficiency and the reproducibility of the analysis may improve as a result.

Isosluotropic mixtures Figure 3.20 is a graphical representation of the eluotropic strength in LSC. This nomogram was originally published by Saunders [358].The solvent strength parameter 8' increases from left to right in the figure as indicated on the top axis. Every other horizontal line represents a particular binary combination of two solvents with the compositions indicated. It is clear that the scale division on these lines, which correspond to eqn.(3.73), is highly non-linear. The vertical dashed line illustrates how a seriesof iso-eluotropic mixturescan be located. Mixtures of about 75% methylene chloride in n-hexane, 49% diethyl ether in n-hexane, 50% methylene chloride in 2-chloropropane, 46% diethyl ether in n-hexane, 1.5% acetonitrile in 2-chloropropane and 0.1% methanol in 2-chloropropane all show similar solvent strengths (8= 0.30). As in RPLC, these iso-eluotropic mixtures are expected to yield similar capacity factors, but may give rise to certain specific effects towards certain (types of) solutes, which may be exploited to enhance separation. Of the many different iso-eluotropic solvent mixtures, not all are equally attractive from solvent strength

(silica)

.05 .10 .15 .20 .25 .30 .35 .LO .L5 .SO .55 .60 .65 .70 .75

0510 01 3 5

l ' f i ' 1

01 3 5

50 I

: I Il%Et20inHx 3odm

1 p -

ON)

in H~

:1w

yz in i Pr CI

I I I % EtzO in iPrCl

,*,I, I

0 .5 1 i2'3 5 I0

' Hx ,hexane iPrCI.isopropyl chloride MC,methylene chloride Et20,ethyl ether ACN. acetonitrile MeOH. methanol

-5

;

30 50100

I%ACN~~~P~CI

2 3

zp :050 I

0 60100

100

IOhMeOHiniPrCI

%EtzO in MC

01235 10

lU)

! I %ACN in MC

2; 3p

loo

:IH%MeOHinMC

0 510

l w ] % A C N in EtzO

.5 1

2 3

01 3 5

'p ,

%MeOH in EtzO

, 'P %MeOHin ACN 10

Figure 3.20: Nomogram illustrating the solvent strength of various binary solvent mixtures for LSC. Vertical (dashed) line illustrates a series of iso-eluotropic solvents (see text). Figure taken from ref. [358]. Reprinted with permission.

a practical point of view. Moreover, to allow a reasonably efficient search for optimum conditions, it is necessary to select a few solvents. Glajch et al. [359]have suggested the use of methylenechloride, methyl t-butyl ether and acetonitrile as modifiers in n-hexane (see section 5.5.1). Eqn.(3.73) suggests that any mixture of two solvents with the same 8 value (iso-eluotropic solvents) will also have the same eluotropic strength. This would allow the application of a similar strategy for the definition of iso-eluotropic multicomponent mobile phase mixtures as was used for RPLC in section 3.2.2.1. In practice, the situation in LSC has proved to be more complicated, because an effect described as â&#x20AC;&#x153;solventlocalizationâ&#x20AC;? limits the validity of eqm(3.72) and (3.73) if polar components (such as acetonitrile or methyl t-butyl ether) are present in the mobile phase. This makes it difficult to calculate the composition of iso-eluotropic mixtures for LSC with sufficient accuracy for optimization purposes [360-3631. In practice, as a first approximation, it may be assumed that mixtures of iso-eluotropic solvents can be used. If the resulting solvent strength is either too high or two low, it may be corrected by the addition of more or less n-hexane. The stationary phase

For many years silica has been the dominant adsorbent used in LSC. Silica has the advantage of abundant availability. It can be obtained commercially in different particle sizes (spherical or aspheric materials), different specific surface areas and different pore size distributions. Because the specific surface area is usually large (up to about 400 m2/g), the sample capacity of silica is relatively high. A disadvantage of the availability of many different silicas is the limited reproducibility of the packing materials. Apart from the factors described above, the chromatographic behaviour of the silica can be affected by chemical factors such as the structure of the surface (affected by heat treatments and by washing the column with acidic or basic solutions), the history of the material (previous usage) and the presence of contaminants (e.g. metal ions). The water content is another major factor. Physically adsorbed water can be removed from or added to the surface, but water bound to the surface as silanol groups â&#x20AC;&#x2DC;(chemisorption) cannot be introduced or removed once the silica is packed into the column. In general, different silicas from different manufacturers may show large differences in retention and selectivityand even between different batches of the same (nominal) product from the same manufacturer the differences may be considerable. For these reasons, it is often necessary to re-optimize the separation (mobile phase) if a new column is installed for an existing separation method. Historically, alumina used to be one of the standard adsorbents for LSC. Snyder (ref. [350], chapter 11) has compared the chromatographic selectivity of silica and alumina surfaces extensively. Alumina may offer some advantages over silica, especially for separations that can be enhanced at high pH values. In recent years therefore, there has been a revival of interest in alumina and its applications in LC [364]. Another material that has recieved considerable attention in recent years is carbon [365]. Carbon can be used as an adsorbent for LC in one of several forms, such as pyrolytic carbon (either as such or as a thin layer covering silica particles), glassy carbon and 81

graphitized carbon. An especially interesting carbon material for LC appears to be the porous graphitized carbon (PGC) described by Gilbert et al. 13661. The advantages of carbon surfaces are their chemical inertness and stability. However, it is difficult to prepare carbon packings with the same specific surface area, pore size (distribution) and pore volume as typical silicas. Moreover, although purely carbonaceous materials will in theory be highly non-polar reversed phase materials, all materials prepared so far are found to behave as fairly polar surfaces, requiring fairly non-polar (high methanol content) mobile phases for the elution of the solutes. Figure 3.8 suggests that the present carbon-based materials are most useful for the RPLC separation of polar compounds. Temperature

The effects of temperature in LSC are similar to those observed in RPLC. Eqn.(3.57) may be used for a quantitative description. The temperature is usually not considered to be a relevant parameter. A typical change of 2% in k for 1 "C variation in the temperature (ref. 13491, p.390) may, however, warrant a careful control of the column temperature.

3.3 SEPARATION OF IONS IN LC The LC methods discussed before were based mainly on physico-chemicalinteractions between the solute on the one hand and the two chromatographic phases on the other. Although we have seen that in RPLC the degree of ionization of weakly acidic or basic solutes may be a major factor in the control of retention and selectivity, the ionic species themselves were not exploited purposefully to realize or enhance the separation. In fact, in a typical RPLC system all fully ionized solutes will show little retention and therefore little resolution can be achieved between different ions. The methods described in this section make positive use of the ionic character of solutes to create a chromatographically selective system. 3.3.1 Ion-exchange chromatography (IEC)

In ion-exchange chromatography (IEC) ionic or, rather, ionizable groups (R) are permanently present on the surface of the stationary phase. In the absence of the solute, these groups are all masked by a counterion (0, which is present in the mobile phase in a constant concentration. Retention is based on an opposite charge between the solute ion (denoted below as the anion X- or the cation YH+) and the ionic groups on the stationary phase. The counterion has a charge similar to that of the solute ions. Typically, the following schematic reactions can be used to describe the IEC process: E

+ X- 3 R + X - + u3 R - U + + YH+ e = R-YH+ +

R+U-

(3.75)

U+.

(3.75a)

In the first case we speak of anion-exchange, since the exchanged ions U- and X - are negatively charged. The second reaction illustrates a cation-exchange process. It is clear that different stationary phases will typically be used for the two types of IEC. Thus, there 82

fraction cahon exchanger strong 0

weak

weak 0

12 PH

Figure 3.21: Variation of the capacity (fraction of charged functional groups) of typical ion-exchange materials with the pH of the mobile phase. Top: cation-exchangers; bottom: anion exchangers. Ionized fraction is fraction associated with counterions. Remaining fraction is associated with H30+ or OH- ions.

are anion-exchange columns, with positive groups on the surface, and cation-exchange columns with negative groups. A further differentiation can be made from a classification in strong and weak ion-exchange materials. A strong ion-exchanger possesses functional groups which are always ionized. This implies that over the practical range of pH values the capacity of the stationary phase remains unaltered. Weak ion-exchangers are affected by the pH. Weak cation-exchangers gradually lose their exchange capacity if the pH is decreased. With weak anion-exchangers this occurs when the pH is increased. The variation of the degree of ionization of the functional groups on the surface, a quantity that is directly proportional to the ion-exchange capacity, of some typical stationary phases is illustrated in figure 3.21. Examples of the different kinds of exchangers are given in table 3.5. The different stationary phases can also be classified on the basis of their physical structure. Pellicular materials, the particles of which consist of a hard (glass) core covered by a thin layer of an ion-exchange resin, may be used if a moderate efficiency and a small ion-exchange capacity are acceptable, but not if the column is required to have a high Table 3.5:

Examples of different types of ion-exchange materials. ~~

Anion

Cation Strong

Sulfonate

- so,

Quaternary amines

- NR:

Weak

Phosphonate Carboxylate

- Po;-

Tertiary amines Secondary amines

- NRZ - NR+

-coo-

stability. Glass beads covered with a styrene-divinylbenzene cross-linked copolymer backbone to which the functional (ion-exchange) groups are chemically bonded may be employed over the entire range 1 < pH < 13 [3671. As an alternative to pellicular materials, microparticulate stationary phases may be used. These are either based on organic resins or on inorganic oxides. The latter class contains bare oxides, as well as chemically bonded phases, which may be synthesized in a way similar to that described in section 3.2.2.1, but the functional end group is now an ionic one. Resin based materials offer a greater chemical stability (large pH range), whereas silica based materials are mechanically more stable and allow a wider range of (organic) solvents to be used. All microparticulate phases offer a high column efficiency and a large ion-exchange capacity. Therefore, in modem HPLC they are usually preferred to pellicular packings. The retention and selectivity in IEC are influenced by a number of parameters, which we will discuss below.

Counterion concentration The concentration of the counterion can be used to control the retention in IEC. It plays a role similar to that of the eluotropic strength of the eluent in RPLC or LSC, in that it affects retention much more than it does selectivity. The capacity factor can be related to the distribution coefficient of the solute ( D J (3.76)

k = D,(V,/V,J.

D, is the ratio of the total concentrations of solute ions in the two phases. The total concentration may involve “free” ions, protonated ions, absorbed molecules and all other forms of the sofute ion X: D, =

rlr.],,,.

I:[“A?’], / I:

(3.77)

For the exchange of strong ions on strong exchangers very simple equations result: D, = [RxJ / [ X - 1

(3.78)

for (monovalent) anions or

D, = [RYH] / [YH+]

(3.78a)

for cations. For a weak monovalent anion the situation is slightly more complex and the distribution coefficient becomes

A similar equation can be written for a weak cation: (3.79a) 84

If we introduce the exchange equilibrium constant ( Km), which reads for monovalent anions (see eqn.3.75) (3.80) then we find with eqn.(3.78) (3.81) and with eqn.(3.79) (3.82) where K,,is the acid dissociation constant for solute X(eqn.3.61). A similar equation can readily be derived for cations. From eqm(3.81) and (3.82) it is clear that for monovalent counterions, D (and hence the capacity factor k) is inversely proportional to [ U-1, SO that In k = In [U-]+ In k, ,

(3.83)

where k, is the capacity factor observed at a (hypothetical) unit concentration of counterions. According to eqn.(3.83) a plot of In k vs. In [ U-]will yield a straight line, with a slope that is independent of both the kind of solute and the kind of counterion. The slope will only vary if the valence of the solute (a) or the valence of the counterion (b) changes. This can easily be accounted for in eqn.(3.83), which reads for the general case In k = ( a / b ) In [vl -t In k,

(3.84)

The validity of eqn.(3.84) is demonstrated in figures 3.22% b and c. In figures 3.22a and b the retention of some nucleotides in IEC is shown. The counterion is monovalent potassium dihydrogen phosphate. The figure shows a series of straight lines, the slopes of which are in good agreement with the predicted values from eqa(3.84): 0.96 for the monophosphates (solutes 1 to 5), 1.85 for the diphosphate (solute 6) and 3.03 for the triphosphate (solute 7). Figure 3 . 2 2 ~illustrates the validity of eqn.(3.84) for the IEC separation of some inorganic anions. The counterion in this example is a mixture of monovalent and divalent phthalate ions. At the selected pH of 5.3 the average charge of the phthalate ions is 1.52. According to eqn.(3.84) this would result in slopes for monovalent solute ions of about 0.66 and about 1.3 for divalent ions. These figures correspond reasonably well with what is observed in figure 3.22b [3681. From eqn.(3.84) and figures 3.22a, b and c we conclude that the concentration of counterions in IEC is a primary parameter which may be used to vary retention, i.e. to bring the capacity factor into the optimum range. Only the selectivity between solutes of different valencies will be affected considerably by changes in the concentration of the counterion. 85

lo1

‘.

Figure 3.22: (a) and (b) Examples of the variation of retention (log k) with counterion concentration (log c) for nucleotides according to eqn.(3.84). Mobile phase: potassium dihydrogen phosphate in water, pH=3.15. Stationary phase: Perisorb AN. Solutes: 1 = thymidine 5’-monophosphate, 2 = ribothymidine 5’-monophosphate, 3 = deoxyuridine 5’-monophosphate, 4 = deoxyguanosine 5’-monophosphate, 5 = guanosine 5’-monophosphate, 6 = guanosine 5’-diphosphate, I = guanosine 5’-triphosphate. Figures taken from ref. [357]. Reprinted with permission. (c) (see opposite page) Examples of the variation of retention (log k) with counterion concentration (log c) for some monovalent and divalent inorganic anions according to eqn.(3.84). Mobile phase: Phthalic acid in water (pH = 5.3). Stationary phase: Vydac 302 IC silica-based ion-exchanger. Solutes as illustrated in the figure. System peak corresponds to the retention time of the phthalate ion. Figure taken from ref. [368]. Reprinted with permission.

Mixed retention mechanisms

In the above discussion we have assumed that no other retention mechanisms play a role in IEC other than an ion-exchange process. For instance, we have assumed in eqm(3.78) to (3.82) that other forms of the solute, such as the protonated form of an anion ( H X ) , are not present in the stationary phase. In practice, this assumption is not always correct. For this reason, different’ packing materials with the same functional groups may show different selectivities. For example, Rabel[367]has illustrated the differences in selectivity for the separation of nucleotides on two different strong anion-exchangers.The selectivity on a pellicular material was markedly different from that on a silica-based stationary phase. The percentage of cross-linking in an organic resin may also affect the selectivity [369]. 86

I \*

H2 POL

- 0.2

-0.L -2.7

-26

-2.5

-21,

-23 log -c

-2.2

-23

-2.0

Mixed retention mechanisms are most evident in the separation of polyelectrolytes. These are large, multivalent molecules, which possess polar and non-polar groups (or "sites") on the surface of the molecule in solution, that may interact physically with the backbone of the ion-exchanger. The most important examples of polyelectrolytes are proteins. IEC has long been the major tool for the separation of proteins by HPLC, but it is being replaced more and more by RPLC [344]. One of the reasons for this is that due to mixed retention mechanisms broad and non-symmetrical peaks are common for the IEC separation of proteins. Type of counterion

The type of counterion used may affect the retention considerably. The eluotropic strength of the different counterions is usually expressed as an eluotropic series. An example of this is shown in table 3.6. Also, the type of counterion may have an effect on selectivity. Especially for anions dramatic differetices are sometimes observed (see e.g. ref. [370]). Similarly, the choice of the buffer may have a considerable effect on the selectivity in IEC. Phosphate has been recommended as the most useful general purpose buffering agent 13671. If other buffers are used, the selectivity needs to be re-optimized.

The pH will affect the capacities of weak ion-exchangers as well as the dissociation of weak anions and cations (e.g. eqn.3.82). In these cases, the pH may be the most relevant parameter in the IEC separation process. Analytical equations can be derived for all combinations of solutes, stationary phases 87

and counterions. However,especiallyif we do not limit ourselves to monovalent ions, these equations may become quite complex algebraically. For the simple case of a monovalent anion on a strong anion exchanger using a strong counterion, the relationship is given by eqn.(3.82). We find that the capacity factor of the solute is proportional to the relative dissociation, since the last factor in eqn.(3.82) may be rewritten as

(3.85) This factor will approach unity if [H,O+]4 KQ,x,i.e. pH > pK,,,. Hence, at pH values well above its p K , . , value, the solute will be completely dissociated. At pH = p K , . , the dissociation will be SOo/o and it will further decrease when pH < pK,., Some schematic examples of the effect of the pH on the retention of weak acids and bases on strong ion-exchangers are shown in figure 3.23. On weak ion-exchangers the effective relative dissociation is the product of the dissociation of the solute and that of the stationary phase. The effective relative dissociation is then (3.86) where s denotes the stationary phase (ion-exchanger). This may result in a maximum retention at a particular pH value, as is illustrated in figure 3.24. Table 3.6: Typical eluotropic series for anions and cations in IEC. Ions are listed in order of increasing elution strength. Anions

Cations

Fluoride Hydroxide (OH-) (1) Acetate Formiate Chloride Thiocyanate Bromide Chromate Nitrate Iodide Oxalate Sulfate Perchlorate Citrate Hydroxide (OH-) (2)

Lithium Hydronium (H,O+) (1) Natrium Ammonium Potassium Rubidium Cesium Silver Manganese Copper (11) Calcium Strontium Barium Trivalent anions Hydronium (H,O+) (2)

(1) On stong cation and anion exchange columns. (2) On weak exchangers.

"strong anion exchanger"

&ax

\ \

"strong cation i exdanger"\

8 1 0 1 2 1 L

\ \

8 1 0 1 2 1 L

Figure 3.23: Variation of the capacity factor (relative dissociation coefficient, see eqn.3.85) as a function of the pH for some weak acids and bases on strong ion-exchange materials. p K , values refer to different solutes.

"weak cation

exchanger"

Figure 3.24 Variation of the capacity factor (relative dissociation coefficient, see eqn.3.85) as a function of the pH for some weak acids and bases on weak anion-exchangers @ K b = 6 ; top) and cation-exchangers @ K , = 7; bottom). p K , values in the figure correspond to different solutes.

Figure 3.25 shows an example of the effects of pH in IEC in practice. Temperature

Frequently, IEC separations are carried out at elevated temperatures. This is because the kinetics of the ion-exchange process may be improved dramatically. The efficiency of the column may be increased by a factor of three if the temperature is increased from 30 to 70 O C [3711. An additional advantage of an increased column temperature is a decrease in the eluent viscosity and hence a reduced pressure drop over the column. 89

Increasing the temperatureleads to a decrease in retention. However, in some cases this is accompanied by marked changes in the selectivity (see e.g. ref. [371]). Organic modifiers

Organic modifiers may be added to the mobile phase in IEC in order to optimize the

___)

Figure3.25: Experimental variation of the retention with pH for somenucleobases (a)and nucleosides (b) in IEC. Stationary phase: Aminex A-28. Mobile phase: 5 mM citrate - 5 m M phosphate buffer in 50-50 ethanol-water. Temperature:70 "C. Figure taken from ref. [371]. Reprinted with permission.

selectivity for a particular separation. According to Rabel [367], not more than 10% of modifier may be added, because otherwise the dominant retention mechanism may be partition or adsorption rather than ion-exchange. However, in practice it is not relevant what the mechanism behind a separation is. It is only relevant that optimum resolution is obtained for all solutes. Therefore, the addition of large amounts of organic modifiers may be considered as a parameter for the optimization of IEC separations on inorganic stationary phases (with or without a chemically bonded exchange group). For organic based materials, the amounts of organic modifiers that can be added to the mobile phase may be limited by swelling of the polymer. The addition of organic modifiers may lead to either an increase or a decrease in retention. Moreover, the effects can differ considerably for different solutes, as is illustrated in figure 3.26 for some basic alkaloid drugs using unmodified alumina as the ion-exchange material. The organic modifier content of the mobile phase can be used to optimize the separation. This has for example been shown for alkaloids [373,374] and for nucleosides and nucleobases [372]. Ion chromatography Ion chromatography is a fashionable phrase used for the IEC separation of inorganic ions. Initially [375], the term was used exclusively to describe an ion-exchange LC system, equipped with a special background suppression column and a conductivity detector. The suppression column is used to reduce the conductivity background of the mobile phase. If a weak counterion is used (such as the bicarbonate ion), then an exhange of sodium ions against protons in the suppressor column will lead to a greatly reduced background conductivity. Nowadays, however, ion chromatography may describe any of various techniques for the liquid chromatographic separation of inorganic ions [376]. Therefore, the parameters that are relevant for IEC in general bear the same kind of relevance in ion chromatography. The most prolific application of ion chromatography is the simultaneous determination of a series of common inorganic anions. These include monovalent ions (fluoride, chloride, bromide, iodide, nitrate and nitrite) as well as multivalent ones (sulfate, sulfite, phosphate). Therefore, both the retention and the selectivity are strongly affected by the concentration of the counterion. This is illustrated in figure 3.22~. Usually, the stationary phases for ion chromatography have a low capacity, in order to reduce the background signal in conductivity detection. Selectivity in ion chromatography can be optimized along the same lines as other chromatographic methods [368]. Gradient elution

Many separations in IEC require the use of gradients, i.e. not all components of the sample can be eluted at one given composition of the mobile phase, so that this composition has to be changed during the elution. Since for weak solute ions the pH has the largest effect on retention, pH gradients are the most effective. However, salt (ionic strength) gradients are both more general and more predictable in their effects [377]. 91

I . , , , , , , , . 20 Lo 60 80

MeOH content/%

t i , , . , , , , , 0 20 Lo 60 80 ACN content/%

Figure 3.26: Variation of the retention of alkaloid drugs in IEC with the concentration of various organic modifiers in the mobile phase. Conditions: citric acid and trimethylammonium hydroxide; Figures (a) and (b): 0.01 M, pH=6; Figure (c): (see opposite page) 0.002 M, pH=6. Column: Spherisorb A 10 Y (alumina). Solutes: cocaine( 0 ), dihydromorphine(*), morphine (El), dihydrocodeine (A), ephedrine (0)and brucine (x). Figure taken from ref. (3731. Reprinted with permission. Conclusion

A number of parameters may affect retention and selectivity in IEC. Because of the subtle differences in selectivity between different ion-exchangers, it is often necessary to optimize the separation in a specific situation. The common way to do this [367] is by varying a single parameter at a time, keeping all the others constant. As we will see in chapter 5 (section 5.1.1), this is not the most appropriateway to approach the optimization 92

60 80 THF content/%-

of chromatographic separations, and therefore IEC is one of the techniques that may benefit substantially from a systematic approach to method development and optimization.

3.3.2 Ion-pair chromatography (IPC) Ion-pair chromatography (IPC) is based on the principles of ion-pair extraction [378]. The underlying idea is that in a two-phase (liquid-liquid) system of which one phase is aqueous and the other one organic, ions will predominantly be found in the aqueous layer, and neutral molecules in the organic one. This will be true for most organic molecules, and the more so the larger and the less polar the molecules become. It will also be true for most ions, the more so the smaller and more polar the separate ions (X and r) are. If X- is a solute anion and if Y+ is a so-called pairing ion present in the aqueous phase, then a simple equilibrium scheme for ion-pair extraction can be drawn, as is shown in figure 3.27. In figure 3.27 K%qy is the equilibrium coefficient in the aqueous phase: (3.87)

and K,, it the usual distribution coefficient. In a chromatographic system, the capacity factor will again depend on the distribution coefficient for the solute X, which reads for the example in which the aqueous phase is the mobile one: (3.88)

organic Figure 3.27: Simple mechanism for ion-pair extraction. Ion-pair formation occurs in the aqueous phase. The ion-pair X Y is distributed over the two phases.

If the product K”Xq,[ Y+] < 2, which is usually the case at common concentrations of the pairing ion Y, then eqn.(3.88) simplifies to:

(3.89)

= K , , KIqy [ Y+]

and hence, with eqm(3.76)

K,,

(3.90)

Kyy[ Y+](VJ V,,,)

which for a given solute Xand pairing ion Yon a given column yields a straight line defined by In k = In [Y’]

+ In k, ,

(3.91)

where, as in eqm(3.83) k, is the capacity factor at a (hypothetical) unit concentration of the ion Y. Of course, the above treatment can readily be adapted to account for cationic solutes and to normal phase ion-pair chromatography (NP-IPC), in which the aqueous phase is the stationary one. According to eqn.(3.90), k is proportional to the concentration of the pairing ion, with the proportionality constant being determined by the distribution coefficient for the neutral molecule ( K x y ) and by the dissociation constant for this molecule into the two separate ions X and Y The first factor is affected by the same parameters as retention in the LC of non-ionic solutes (section 3.2). The latter factor will be determined by the nature of the solute ion and the pairing ion and by the composition (ionic strength, pH, modifier content) of the aqueous phase. Above we have described a very simple mechanism for ion-pair extraction. The mechanism in practical IPC experiments is usually not quite as simple. There are several complicating factors. In the first place, we have not considered the pH influence on the dissociation of weak solute ions or pairing ions. The effect of the pH in IPC will be addressed below. aqueous

2“/

Figure 3.28: Illustration of the mechanismof IPC.The solute ion X,the pairing ion Y and the ion-pair X Y are all distributedover the two phases. Ion-pair formation occurs in both phases (reactions along horizontal lines). “Ion-exchange’’reactions may also occur. These reactions involve solute ions in one phase and pairing ions in the other. These reactions can be found along diagonal lines in the figure.

In the second place, we have assumed that both of the ions ( X and Y) are found exclusively in the aqueous phase. This is a great simplification of the true mechanism of IPC. Figure 3.28 shows a more realistic version of figure 3.27. According to figure 3.28 the solute X can be retained by at least three different mechanisms: - Partition of the solute ion between the two phases (characterized by K,) - Ion-pairing between the solute ion X- and the pairing ion Y+ (characterized by KYy), followed by partition of the ion-pair XY over the two phases (characterized by K X Y ) . - Ion-exchange reactions, between solute ions in one phase and pairing ions in the other (these reactions can be found along diagonal lines in figure 3.28 and can be characterized by the ion-exchange equilibrium coefficients K g g and Q). Other reactions, such as the distribution of the pairing ion over the two phases and the two possible ion-exchange reactions in which the pairing ion and not the solute ion transfers from one phase into the other can also take place, but do not have a direct effect on the retention of the solute X. Figure 3.28 reduces to the simple mechanism of figure 3.27 if both K, and K are very small. If K , is small (i.e. the solute molecule is mainly in the mobile phase) but K is large (the pairing ion is mainly absorbed into the stationary phase), then the mechanism of retention in IPC becomes similar to that of IEC. Typical ion-pairing as well as typical ion-exchange mechanisms may play a role in practical IPC systems. Normal phase or reversed phase Both normal and reversed phase separations are possible in IPC. Normal phase systems (NP-IPC) are usually LLC systems. The aqueous phase, containing the pairing ion, is coated onto a silica surface. In order to change the kind or often even the concentration of the pairing ion it is necessary to coat another column. In some cases the pairing ion may be dissolved in the (organic) mobile phase (e.g. long chain fatty acids or amines), but the equilibration of the system will still take a long time. As in all other LLC systems, adequate thermostatting is vital for the performance of the system. A major advantage of the use of normal phase systems may be the possibility to use UV-absorbing (or even fluorescent) pairing ions for the separation of non-UV absorbing solutes. If a UV absorbing pairing ion is in the (aqueous) stationary phase and if this is subsequently eluted from the column as an ion-pair in the presence of sample ions, then a very sensitive detection may be possible (see e.g. ref. [379]). The mechanism of NP-IPC will be very similar to that of ion-pair extraction, i.e. the simple mechanism of figure 3.27. Reversed phase ion-pair systems (RP-IPC) could be of the LLC type, but the use of chemically bonded (alkyl) phases has become increasingly popular, because of the increased stability and flexibility of the system. Even if an LLC system is used for RP-IPC, then a chemical modification of the surface is still required to coat an organic liquid on the particles of (for example) silica. The system is usually equilibrated by adding the pairing ion to the mobile phase and pumping this through until a stable baseline is obtained. Equilibration of reversed phase 95

columns with pairing ions may take up to several hours, depending on the hydrophobicity (chain length) of the pairing ion and on the flow rate. This is much longer than the equilibration times in regular RPLC (without the use of pairing ions), but compares favourably with the effort needed to change the stationary phase in NP-IPC. The most common way to create an RP-IPC system is to use a genuine chemically bonded reversed phase column (e.g. C18; see section 3.2.2.1) and to use large pairing ions with a hydrophobic alkyl chain dissolved in the mobile phase. This technique was introduced by Knox and Laird, who named it soap chromatography [380]. Because of the usuatly long alkyl chains of the pairing ions, the use of C18 phases is to be recommended in order to avoid effects that are related to the critical chain length (see section 3.2.2.1). Table 3.7 summarizes the advantages and disadvantages of NP-IPC and RP-IPC. Because of the ease of operation, the latter technique is currently by far the more popular one. Because of this, most of the following discussion will be focussed on RP-IPC. Table 3.7: Comparison of NP-IPC and RP-IPC systems NP-IPC

RP-IPC

Primary parameters

Organic phase

pH; pairing ion concentration and chain length; counterion concentration

Organic phase

Variable

Fixed

Temperature control

Critical

Not critical

Change kind of pairing ion Change concentration of pairing ion

Difficult Difficult

Easy (1) Easy (1)

Prevailing mechanism

IP-extraction

Dynamic IEC

(1) Equilibration time increases with increasing hydrophobicity (chain length) of the pairing ion.

Effect of pairing ion concentration Because of the complexity of the IPC mechanism, the effect of the counterion concentration is not usually as simple as was suggested by eqm(3.91). One reason for this is that the distribution isotherm for the pairing ion Y is not linear, i.e. K in figure 3.28 is not a constant. Some typical distribution isotherms are shown in figure 3.29. The figure shows that the initial addition of smalt amounts of pairing ion to the mobile phase leads to a predominant absorption of these ions in the stationary phase. However, the stationary phase quickly becomes saturated, the distribution curves flatten and K decreases. Therefore, the effect of changes in the concentration of the pairing ion is bound to be very different at low Concentrations than it is at higher ones. For this reason, 96

10 pm

100

Figure 3.29 Examples of distribution isotherms of a pairing ion (tetrabutylammonium) in a reversed phase system. Left: logarithmic representation; right: conventional (Langmuir) representation. Stationary phase: Lichrosorb RP-18. Mobile phase: indicated percentages of methanol in aqueous phosphate buffer (25 mM H,PO, and 25 mM NaH2P0,, pH = 2.1-3.4, bromide concentration 200 mM. Temperature: 25 "C. Figure taken from ref. [381]. Reprinted with permission.

Crombeen et al. [382] and Bartha er al. [381] have suggested that the concentration of pairing ions in the stationary phase be used as the main descriptive parameter in IPC. However, this parameter is not very convenient in practice, because the distribution isotherms need to be known. In practice, the retention (In k) is usually plotted against the logarithm of the concentration of the pairing ion in the mobile phase (In [ fl). In such plots straight lines (or slightly curved but monotonic lines) are usually observed over wide ranges in concentration. An example is shown in figure 3.30. Kind of pairing ion

Some examples of typical pairing ions are given in tabel 3.8. An extensive list of pairing ions and their applications can be found in ref. [367]. The kind of pairing ion will mainly be determined by the nature of the sample ions. Clearly, for anionic samples a cationic pairing ion will be required and vice versa. Also, if the ions to be separated are small polar ions, then a pairing ion with a large, non-polar group should be used to enhance the extraction of the ion-pair in the organic phase. If the sample ions are large, then small pairing ions may be used. A combination of two large ions is also sometimesused. The resulting ion-pair may have its charge deeply buried, so that it can be extracted with very non-polar solvents. This possibility is of more interest for NP-IPC than it is for RP-IPC, because of the flexibility to choose an appropriate organic solvent in the former technique. The nature of the pairing ion greatly affects retention, but it will also affect theselectivity (e.g. ref. [384]). Each pairing ion will require a different concentration to yield capacity factors in the optimum range. 97

----I

RnlmM

Figure 3.30: Example of variation of retention in IPC with the concentration of the pairing ion (octanesulfonate) in the stationary phase (P; upper of the two horizontal axes) and in the mobile lower axis). The axis for P,is linear, while the one for P,,,is not. Stationaryphase: Hypersil phase (P,,,; O D s . Mobile phase: lOoh methanol in water. Solutes: 1 = homo-vanillic acid, 2 = 5-hydroxyindol-3-aceticacid, 3 = 3,4-dihydroxyphenylacetic acid, 4 = tyrosine, 5 = L-DOPA, 6 = dopamine, 7 = octopamine, 8 = adrenaline, 9 = 3,4-dihydroxymandelicacid, 10 = noradrenaline. Figure taken from ref. [383]. Reprinted with permission.

Table 3.8: Examples of pairing ions for IPC. Pairing ion

Structure

Type

Cations: Tetra-alkylammonium (1) Tri-alkylammonium A1kylammonium

NR: NHR: NH,R:

Strong Weak Weak

Anions:

Chloride Bromide Iodide Perchlorate Alkyl sulfonate Toluene sulfonate Naphthalene sulfonate Alkyl sulfates Alkyl phosphates

c1ClO,

Strong Strong Strong Strong

RSO,

Strong

RSO, RHPO,

Weak Weak

Br-

I-

(1) Either symmetrical ions, such as tetrabutylammonium, or non-symmetrical ones, such as

cetyltrimethylammonium,may be used.

1.6log k

0.8 -

11 13 chain length -

Figure 3.31 :Example of the effect of the chain length of the pairing ion on retention in IPC. Pairing ions: alkyl-benzyl-dimethyl ammonium with different lengths of the alkyl chain. Organic phase: chloroform; Aqueous phase: 0.1 mM of pairing ion in water. Solutes: sodium cromoglycate (circles) and acid red dye I (triangles). Figure taken from ref. [385]. Reprinted with permission.

Influence of the chain length of the pairing ion

A way to influence retention without greatly altering the selectivity is to use different pairing ions from the same homologous series. This offers the possibility to vary the retention more or less continuously. An example of the effect of the chain length of the pairing ion is shown in figure 3.31. It is seen in this figure that approximately straight lines are obtained if the logarithm of the capacity factor is plotted against the chain length of the pairing ion. The length of the pairing should be such as to create a stable system with a good capacity. This implies that one should work on the plateau of the distribution isotherm (figure 3.29). The required chain length will depend on a series of factors, including the type of the pairing ion and the modifier content of the mobile phase. Organic modifiers Organic modifiers may affect both the retention and the selectivity in RP-IPC. Most of all, the amount of modifier added determines the distribution isotherm of the pairing ion and therefore the retention. A secondary factor involves the solubility of the pairing ion in the mobile phase. Large pairing ions may require large amounts of organic modifier to allow them to be dissolved sufficiently in the mobile phase. In principle, the type of organic modifier(s) may be used as a parameter to optimize the selectivity of the RP-IPC system. However, because of the wide choice of other parameters, this possibility has not yet been extensively investigated.

Interdependent parameters From the preceding brief discussion it is apparent that three parameters in RP-IPC are highly intertwined and cannot be chosen independently: 1. the type and concentration of the pairing ion 2. the chain length of the pairing ion 3. the organic modifier content of the mobile phase.

To find a compromise for a mobile phase with neither too large a chain length (because of slow equilibration) nor too high a modifier content (because of the suppression of ionization), but yet optimum capacity factors and stable operating conditions is an optimization problem on its own.

As soon as weak solute ions or weak pairing ions form part of the system, the pH is a vital parameter in the optimization of IPC separations. Often it is a very selective parameter, when the different solute ions have different p K , values. The use of silica based reversed phase packings limits the variations of the pH to the range between about 2 and 7. Because of this limited range of operation, basic solutes often require the use of ion pairing reagents in RPLC, because they are fully ionized in the practical pH range, and give rise to highly non-symmetrical peaks in conventional RPLC.

Kind of buffer The buffer used in RP-IPC has a minor effect on the selectivity. Therefore, the choice of the buffer will be mainly determined by practical considerations, especially by the solubility in the mobile phase. Phosphate and citrate buffers allow a wide range of pH to be used. Acetate buffers are also frequently employed. The buffer concentration should be sufficient to yield a stable system after injection of the solute, but has an otherwise negligible effect on retention and selectivity if the counterion concentration is kept constant (see below). Counterion concentration As in IEC, the counterion concentration has a considerable effect on the retention in IPC. In IPC the counterion is charged similar to the solute molecules, but opposite to the pairing ion. For example, for the separation of anionic solutes, the pairing agent may be a sodium sulfonate, in which the sulfonate is the pairing ion and sodium the counterion. The addition of a buffer salt (e.g. sodium phosphate) and a neutral salt (e.g. sodium bromide) may also contribute to the concentration of the counterion. Because of the similar retention mechanism, the counterion concentration has a similar effect on retention and selectivity in RP-IPC as in IEC. The practice to keep the total concentration of the counterion constant by adding varying amount of the neutral salt leads to a more regular behaviour of the RP-IPC system and is therefore to be recommended [386]. 100

Temperature The temperature wiil affect both retention and efficiency in IPC, but not to the same extent as it does in IEC. IPC is usually a much more efficient technique (in terms of plate counts) than is IEC and therefore ambient temperatures usually yield satisfactory results.

Summary The preferrred form of ion-pairing chromatography is RP-IPC. This is a complex chromatographic method. Unlike in other kinds of chromatography, there is notone but a series of primary parameters (type, concentration and chain length of the pairing ion, pH, organic modifier content) which together determine the capacity factors, but also may give rise to large variations in the selectivity. As in RPLC, the type of organic modifier may be used to optimize the selectivity of the system.

3.4 SUPERCRITICAL FLUID CHROMATOGRAPHY (SFC) In supercritical fluid chromatography (SFC), the mobile phase is neither a gas nor a liquid. The definition of a supercritical fluid can be illustrated in a classical p- T diagram such as figure 3.32. In this figure three phases are located in their specific domain: the solid phase (S), the gas phase (G) and the liquid phase (L). At the triple point (tp) all three phases may coexist. The line that separates the gas and the liquid phase is the vapour pressure curve. This line ends at the critical point cp. Above this point, no distinction can be made between the gaseous and the liquid state. A compound for which either the pressure or the temperature is above the critical value can therefore not be identified as a liquid or a gas. The term supercritical fluid is usually reserved for those conditions at which both the pressure and the temperature exceed the critical value. This area in figure 3.32 can be found in the top right comer and is bounded by the two dashed lines. These dashed lines do not correspond to a phase change between conditions on either side. As was shown by Lauer et al. [387], there is a gradual change in the solvent properties (e.g. density, viscosity) if we

T-

Figure 3 . 3 2 Phase diagram illustratingthe domains of the solid (S), gaseous ( G )and liquid (L) phases as a function of pressure (p) and temperature (7). tp is the triple point, at which three phases co-exist. cp is the critical point, which forms the end of the vapour pressure curve (between tp and cp). The area in the top right corner indicated by SF represents the domain of supercritical fluids. 101

pass the dashed lines under conditions of constant pressure (moving horizontally in figure 3.32) or constant temperature (moving vertically). Retention in supercritical chromatography is affected by the nature of both the mobile and the stationary phase. A variety of stationary phases, including high boiling liquids, polymer films, solid supports and chemically bonded monolayers, has been used. The choice of possible mobile phases is more limited. The critical properties (critical pressure pc and temperature TJ should be within practical reach. Moreover, stable compounds are required, which do not show disintegration at elevated temperatures and pressures. Also, the mobile phase must not be too agressive towards the materials used in the column (usually silica-based phases) and the instrumentation (mainly stainless steel). Therefore, mobile phases that are extremely interesting from a chemical point of view, such as supercritical ammonia and, especially, supercritical water, have found little use so far. Table 3.9 lists some possible mobile phases for SFC together with their chemical properties. There are several reasons why SFC may gain its place as a separation technique alongside GC and LC in the years ahead. From a fundamental point of view, the diffusion coefficients under typical SFC conditions are lower than those typically encountered in gases, but higher than those found in liquids. The viscosity of supercritical fluids is usually higher than that of typical gases, but much lower than that of common liquids. At the same time, supercritical fluids are good solvents for many low-volatile solutes, which are not compatible with GC. Therefore, SFC may offer the possibility to separate non-volatile Table 3.9: Some suggested solvents for SFC. Data taken from refs. [388] and 13891. Asterisks indicate preferred solvents.

Carbon dioxide* Nitrous oxide

31.0 36.4

72.8 71.5

Ethane Ethene n-Butane &Butane n-Pentane* n-Hexane

32.2 9.2 152.0 134.9 196.5 234.2

48.2 49.7 373 36.0 33.3 29.3

Diethyl ether THF Ethyl acetate Acetonitrile Methanol 2-Propanol Ammonia Water

193.5 267.0 250.1 274.8 239.4 235.1 132.4 374.1

35.9 51.2 37.8 47.7 79.9 47.0 111.3 217.6

102

samples much faster and/or more efficiently (higher numbers of theoretical plates) than with LC. From a practical point of view, SFC may allow the use of many different detection principles, including both typical LC detectors (UV-absorbance, fluorescence)and typical GC detectors (flame ionization, mass spectrometry). Also, capillary SFC seems to be well within the posssibilities of current technology, while capillary LC is not. Promising applications of SFC include group separations (paraffins, olefins and aromatics) in petrochemical samples, monitoring of supercritical extraction processes (caffeine from coffee, nicotine from tabacco) and oligomer separations. However, it is in the field of applications that SFC has yet to prove its value. Unique separations that can be accomplished with SFC, but not with either GC or LC, have yet to be demonstrated. The mobile phases that have been used most extensively to date are n-pentane and carbon dioxide. Pentane has the advantage that it is a liquid under ambient conditions, so that it can be handled and pumped in the same way as mobile phases for liquid chromatography. On the other hand, its critical temperature is relatively high (almost 200 "C) and it is a highly inflammable compound. Carbon dioxide has a vapour pressure of about 50 bar at room temperature. It is therefore more difficult to handle, and it can only be pumped as a liquid when it is cooled down to sub-ambient temperatures. However, carbon dioxide is non-flammable and non-toxic, which makes it very attractive from a practical point of view. Also, the critical properties of carbon dioxide are very mild. Mobile phase density

The main factor that influences the retention in SFC is the density of the mobile phase. For a given eluent, the density is a function of the pressure and the temperature. At a given temperature, the retention varies with the pressure in a rather coomplicated way, as is illustrated for the retention (In k) of naphthalene using CO, as the mobile phase in figure 3.33a. Figure 3.33b represents the same data, but now retention is plotted against the density of the mobile phase. It is seen that smooth curves are obtained, which hardly vary with the temperature. Of course, to obtain the same mobile phase density, a much higher pressure is required when the temperature is increased from 35 to 50 OC. Figure 3.33b is seen to be very similar to a typical plot of retention (In k) vs. composition (p) in RPLC (see e.g. figure 3.14). Hence, a quadratic equation may be used to describe the relationship between retention (In k) and density @) in S F C (3.92) Composition of the mobile phase

Both pentane and carbon dioxide are solvents of low polarity. The polarity may be increased by the addition of suitable modifiers to the mobile phase. Such modifiers have a pronounced effect on the retention. The decrease in retention upon the addition of modifiers seems to resemble what is observed in LSC (see section 3.2.3). Apart from the effect on retention, the addition of polar modifiers to the mobile phase also has a marked effect on the peak shape. Especially in the case of more polar solutes, the addition of 103

modifiers to the mobile phase has become increasingly popular. The nature and concentration of organic modifier is a parameter that may be used for the optimization of SFC separations. Some initial work in this direction has been reported by Randall [392].

1 0 30 do 50 60 70 80 90 100 110 120

-2.5

platm

3.02.5

2.0 -

logk

1.5-

1.0 -

0.5 -

0.0 0.5 -1.0 -1.5 -

2 -0.-

-2.0 -1.6

-1.2

-0.8

-0.L

Figure 3.33: Retention (In k ) as a function of (a) pressure, (b) mobile phase density and (c) the logarithm of the mobile phase density in SFC at three different temperatures.Mobile phase: carbon dioxide. Stationary phase: ODS. Solute: naphthalene. Figure taken from ref. [390]. Reprinted with permission. Experimental data from ref. 13911.

104

Stationary phase effects It is not yet clear what type of stationary phase will be most useful for SFC. Liquid stationary phases will almost inevitably be of insufficient stability. Polymeric films of various thickness and varying degree of cross-linking have been used. Preferably, such polymeric phases should be covalently bonded to the column wall (open columns) or a solid support (packed columns). Alternatively, solid adsorbents or chemically bonded monolayers may be applied. To a first approximation [393] the selectivity (a) on a given stationary phase may be expected to be independent of the mobile phase density. Consequently, the problem of stationary phase selection is similar to that encountered in GC. In GC each stationary phase will require a given temperature at which the capacity factors are in the optimum range. In SFC, each stationary phase will require a given mobile phase density. Different phases may be compared at their individual optimum conditions.

3.5 CLASSIFICATION OF PARAMETERS In this chapter we have discussed the parameters that affect the selectivity in various chromatographic methods. The parameters we have encountered can roughly be divided into three categories: 1. Thermodynamic parameters (T). These include temperature and pressure. 2. Stationary phase parameters (S), which include the nature and composition of the stationary phase. 3. Mobile phase parameters (M) which include the nature and composition of the mobile phase, pH, nature and concentration of additives such as buffers, salts, ion-pairing agents or complexing agents. Two further categoriesof parameters may be defined, which do not affect the selectivity:

4. Capacity parameters (C) i.e. those parameters which affect the phase ratio: film

thickness, surface area, column diameter (open columns), porosity (packed columns).

5. Physical parameters (P) column length, flowrate, particle size, column diameter

(packed columns).

The capacity parameters do not affect the selectivity (a),but they do have an effect on the capacity factor ( k ) and hence on the resolution (Rs;see eqn.1.22). The physical parameters only affect the resolution through the efficiency ( N ) . They also have an effect on the retention time through the hold-up time to (see eqn.l.6). Physical parameters may be used to trade off increased resolution against decreased analysis time. Ideally, this is done separately from the selectivity optimization process, because the effects are simple, predictable, and independent of the parameters that do affect the selectivity. Independent parameters with a simple effect on the resolution may be optimized sequentially, i.e. one after the other (section 5.1.1). Hence, after the selectivity has been optimized, the shortest possible column length or the highest possible flowrate may be established that will provide sufficient resolution. Adapting the length of the column is the preferred strategy, because it will lead to both faster analysis and lower pressure drops. 105

Some further comments on optimization of the physical parameters will be made in chapter 7. The capacity parameters allow a variation of the capacity factor (and hence the resolution) independent of the selectivity. However, all these parameters are difficult to vary, since they almost always require new columns to be used. Moreover, the range of variation offered by these parameters is too limited for them to be generally useful in optimization schemes (see also section 4.2.3). Therefore, the thermodynamic parameters (T), the stationary phase parameters (S) and the mobile phase parameters (M) are the ones we should consider if we wish to select the most relevant parameters for the optimization of chromatographic selectivity. Of these three categories the thermodynamic parameters can be varied most easily. However, temperature has a major effect on retention in GC,but only a minor effect on the selectivity. In LC its effect is never very large, except from some ionic separations. Pressure is only relevant as a parameter for SFC.We conclude that temperature should head the list of optimization parameters in GC,and pressure (possibly in combination with temperature) in SFC. Stationary or mobile phase optimization

In GC we cannot use the nature and composition of the mobile phase to vary the selectivity. Hence, the nature and consequently the composition of the stationary phase should be used for optimization purposes. There are many more stationary phases Table 3.10a: Summary of parameters for selectivity optimization. Asterisks indicate preferred parameters. Method: Gas Liquid Chromatography (GLC) Gas Solid Chromatography (GSC) Section: 3.1.1 and 3.1.2 Primary parameter(s)

Suggested relationship

Type Parameter

Plot

Shape

Eqn.no.

In(k/T) vs. 1 / T k vs. d,y

linear linear linear

3.10

Temperature * Film thickness Surface area

k vs. s

Secondary parameter(s)

Suggested relationship

Type Parameter

Plot

Shape

Eqn.no.

Sd Sc

k vs. cp

linear

3.14

106

Stationary phase Stationary phase composition

Table 3.10b: Summary of parameters for selectivity optimization. Asterisks indicate preferred parameters. Method: Liquid-Liquid Chromatography (LLC) Section: 3.2.1 Primary parameter(s)

Suggested relationship

Type Parameter

Plot

Shape

Eqn.no.

k vs. V J V ,

linear

1.10

Mc Sc Cc

Polarity of mobile phase * Polarity of stationary phase Phase ratio

Secondary parameter(s)

Suggested relationship

Type Parameter

Plot

Shape

Eqn.no.

In k vs. 1/T

linear

3.57

Md Sd Tc Mc Mc

Nature of mobile phase * Nature of stationary phase Temperature PH (1) Ionic strength (1)

(1) May be used if the more polar phase is aqueous.

available than could possibly (or, indeed, sensibly)be tried. After some different stationary phases (see section 2.3.1) have been tried, the possibility of using a mixture of two stationary phases could be considered as a final step in the optimization. In LC we have a choice between optimizing the stationary phase parameters or the mobile phase parameters. Obviously, the latter can be changed more readily. Advantages of mobile phase optimization are: 1. many parameters offer a great flexibility, 2. the mobile phase can easily be changed, 3. there are good possibilities for automation, 4. the investment required for columns is low. On the other hand, if the stationary phase parameters are being optimized, other advantages may occur: 1. stable and reproducible operation with simple mobile phases is possible, 2. mobile phases may be selected with a low cost, low viscosity and low toxicity. Hence, optimization of the mobile phase offers advantages mainly during the optimization process, while optimization of the stationary phase offers its main advantages after the optimization. So far, researchers have been more concerned with the optimization process 107

itself than with the usefulness of their results. Hence, the mobile phase parameters have been optimized almost exclusively. In the future we may see an increased use of the optimization of stationary phase parameters, especially on the part of column manufacturers. This will result in the availability of reproducible systems for optimized separations on dedicated stationary phases for GC as well as for LC. 35.1 Summary of parameters for selectivity Optimization

Table 3.10 summarizes the parameters of interest for the various chromatographic techniques described in this chapter. A distinction is made between primary and secondary parameters. Table 3.10~: Summary of parameters for selectivity optimization. Asterisks indicate preferred parameters. Method: Reversed Phase Liquid Chromatography (RPLC) Section: 3.2.2 Primary parameter(s)

Suggested relationship

Type Parameter

Plot

Shape

Eqn.no.

In k vs. cp In k vs. cp (1) In k vs. pH

quadr. linear curved

3.38 3.45 3.631 68/70

Mc Mc

Mobile phase polarity (modifier content) or PH (2)

Secondary parameter(s)

Suggested relationship

Type Parameter

Plot

Shape

Eqn.no.

In k vs. 1/T

linear

3.57

In k vs. ne In kvs. I

linear (4) hyperboiic

3.71

Mc Tc Sd Sd Ss Mc Md

Nature of modifier(s) (3) * Ratio of modifier concentrations.* Temperature Nature OF stationary phase Nature of buffer Stationary phase chain length Ionic strength Nature of buffer

( 1 ) Linear approximation for 1 < k < 10. (2) pH is a primary parameter for ionizable solutes.

(3) Modifier coontent f a - multicomganent mobile phases can be estimated using table 3.1, (4) Approximately linear up to â&#x20AC;&#x153;critical chain lengthâ&#x20AC;? (see section 3.2.2.1).

108

Table 3.10d: Summary of parameters for selectivity optimization. Asterisks indicate preferred parameters. Method Liquid-Solid Chromatography (LSC) Section: 3.2.3 Primary parameter(s)

Suggested relationship

T v ~ e Parameter

Plot

Shape

Eqn.no.

In k vs. In X ,

linear

3.74

Eluotropic strength

Secondary parameter@)

Suggested relationship

Type Parameter

Plot

Shape

Eqn.no.

Md Md Tc Sd

In kvs. 1 / T

linear

3.57

(1)

Nature of modifier(s)* Modulators (1) Temperature Nature of stationary phase

Modulators are compounds which can be added to the mobile phase in small quantities to affect peak shape and/or selectivity (e.g. water, tri-ethylamine).

Primary parameters are those which have a large effect on retention. Usually, these parameters d o not affect selectivity to the same extent. Therefore, these are the parameters that can be used to bring the capacity factors of the solute into the optimum range. Secondary parameters may affect retention, but always affect selectivity. In fact, ideally the parameters should be selected such that the retention ( k ) is kept roughly constant (i.e. in the optimum range) while the selectivity (a)can be varied. If the secondary parameters d o affect retention, then sometimes this ideal situation can be approached by the simultaneous variation of two (or more) parameters a t the same time. Examples of this may be found in chapter 5. Capacity parameters are not often used as primary optimization parameters in chromatography. Therefore, they are only included in table 3.10 in those cases in which they are used with some frequency. It should be noted, however, that changing one of the capacity factors usually involves the use of a completely different column and is therefore unattractive. Although changing the capacity parameters affects retention in a n essentially predictable way, changing the column (packing material, film thickness, etc.) may give rise to unexpected second order phenomena. This is a second reason for which capacity parameters should not be recommended as primary optimization parameters. Parameters that affect neither the capacity factors nor the selectivity (such as column length or flow rate) will not be found in this table. The parameters are classified by two different letters. The capital letters correspond to the classification given above, i.e. thermodynamic parameters (T), stationary phase

parameters (S), mobile phase parameters (M), capacity parameters (C) and physical parameters (P). The lower case letters indicate a second classification of the parameters. Three different types of parameters are indicated: - continuous parameters (c), which can take on all values between given limits (e.g. temperature), - discrete parameters (d), which can only take on certain values (e.g. the kind of stationary phase), - stepwise parameters (s), which can take on a series of discrete values (e.g. the chain length of alkylsulfonate ions in ion-pair chromatography). Table 3.10a lists the parameters that may be used in the two modes of GC discussed in this chapter (GLC and GSC). Because of the similarity of these two techniques, they have been combined in one table. To optimize the capacity factors, the temperature may be adapted. Temperature is the most commonly used primary parameter in GC. Alternatively,the film thickness (in GLC) or the surface area of the stationary phase (in GSC) may be used to change the capacity Table 3.10e: Summary of parameters for selectivity optimization. Asterisks indicate preferred parameters. Method Ion Exchange Chromatography (IEC) Section: 3.3.1 Primary parameter(s)

Suggested relationship

Type Parameter

Plot

Counterion concentration pH(l)* Exchange capacity

In k vs.ln[ v] In k vs. pH k vs. capacity

Secondary parameter@)

Shape

Eqn.no.

linear sigm. linear

3.84 3.85/86

Suggested relationship

Type Parameter

Plot

Shape

Eqn.no.

In k vs. l / T

linear

3.57

Tc Md

Mc Md Md

Temperature Type of modifier(s) Concentration of modifier(s) Type of counterion Type of buffer Type of stationary phase

(1) pH is a primary parameter if weak solutes, counterions or ion-exchangers are involved in the separation process.

110

Table 3.10f: Summary of parameters for selectivity optimization. Asterisks indicate preferred parameters. Method: Ion Pairing Chromatography (IPC) Section: 3.3.2 Primary parameter(s)

Suggested relationship

Type Parameter

Plot

Mc Ms Mc Mc

pH(l)* Chain length of pairing ion Pairing ion concentration * Modifier content *

In In In In

k vs. pH kvs. n, k vs.ln [ r] k vs. cp

Shape

Eqn.no.

sigm. linear curved quadr.

3.38

Secondary parameter(s)

Suggested relationship

Type Parameter

Plot

Shape

Eqn.no.

In k vs. 1 / T

linear

3.57

Md Md Md Mc Md Tc Sd

Type of pairing ion * Type of modifier * Type of counterion Conc.of counterion Type of buffer Temperature Type of statationary phase

factors. However, in order to change either of these parameters another column is required. Because of the availability of packing materials, the surface area is a discrete parameter. The most common secondary parameter is the kind of stationary phase used, which is obviously a discrete parameter. Because the capacity factors will usually differ on different phases, several parameters will have to be varied at the same time. For example, if another stationary phase is chosen, the temperature may be adapted to bring the capacity factors back into the optimum range. Table 3.10b lists the optimization parameters that may be used in LLC. Clearly, the polarities of the two phases largely determine retention and selectivity. The exact composition of (preferably) the mobile phase may be varied to optimize the separation (i.e. variations in the nature and the concentration of mobile phase components, without substantial variations in the polarity). Even if the temperature is not a major optimization parameter, adequate temperature control is required in all LLC experiments. Therefore it may be experimentally straightforward to exploit temperature as a secondary optimization parameter. Table 3 . 1 0 ~lists the relevant parameters for RPLC. The polarity (modifier content) of the mobile phase is the main primary parameter for most samples, although for some 111

weakly acidic or basic solutes the pH may have an even larger effect on the capacity factors. A series of secondary parameters may be exploited. Changing the nature of the organic modifier is the most common and probably the most rewarding parameter to use. If ternary and quaternary mobile phases are considered, then the ratio between the concentrations of different modifiers becomes a continuous parameter that may be optimized. Most separations are optimized by considering solely the influence of the concentration of modifier(s) in the mobile phase and the pH. However, for particular (or particularly difficult) separation problems there is a series of additional parameters that might be considered. Table 3.10d lists the parameters for LSC. Again, most separations may be optimized by optimizing the eluotropic strength (primary parameter) and the nature (secondary parameter) of the mobile phase. The latter parameter involves the preparation of different iso-eluotropic mixtures containing different solvents, or small quantities of very polar components ("modulators"). As in the case of RPLC, there are several additional parameters that are not frequently exploited. Polar chemically bonded stationary phases (section 3.2.2.2) may be used as an alternative stationary phase for both RPLC and LSC, if variations in the mobile phase do not result in an adequate separation. If polar CBPs are used in combination with more polar mobile phases (reversed phase mode), then table 3.10~may be used to find the most appropriate optimization parameters. If operated in the normal phase mode, table 3.10d Table 3.10g: t Summary of parameters for selectivity optimization. Asterisks indicate preferred parameters. Method: Supercritical Fluid Chromatography (SFC) Section: 3.4 Primary parameter(s)

Suggested relationship

Type Parameter

Plot

Shape

Eqn.no.

In k vs. p In k vs. Q,

quadr. curved

3.92

Mc Mc

Density (I) * Concentration of modifier

Secondary parameter(s)

Suggested relationship

Type Parameter

Plot

Md Sd Md

Shape

Eqn.no.

Nature of mobile phase Nature of stationary phase Type of modifier *

(1) The mobile phase density is determined by the combination of the pressure and the temperature.

112

may be used. However, it should be noted that strictly speaking we do not deal with liquid-solid chromatography. A notable difference is that the water content of the mobile phase has a much less dramatic influence in normal phase LBPC than it has in LSC. The parameters that play a role in ion-exchange chromatography (IEC) are summarized in table 3.10e. A combined optimization of the two primary optimization parameters (pH and counterion concentration) may already be used to optimize the chromatographic selectivity of the system. However, different buffers or counterions are often investigated for their effect on the selectivity. As a rule, elevated temperatures are used to increase the efficiency rather than the selectivity of the system. Table 3.10f lists the most relevant parameters for ion-pairing chromatography (IPC). Here there are four major primary parameters, which cannot be seen as independent. Hence (see section 5.1.l), these four parameters should preferably be optimized simultaneously. Sensible upper and lower limits may be set for each of the parameters and an optimized separation may result from the process. If this is not the case, there are still many secondary parameters that could be exploited. Tables 3.10e and 3.10f suggest that the ionic separation methods IEC and IPC are the most complicated ones. Both methods involve several mutually dependent primary parameters and a series of additional secondary optimization parameters. Therefore, these techniques are bound to be the subject of many optimization studies in the future. Finally, table 3.10g shows the relevant parameters for SFC. The density of the mobile phase (determined by the combination of pressure and temperature) is the main parameter for this technique. Several possible secondary parameters are listed in the table. Because SFC is not yet a mature technique, the list of secondary parameters may still undergo some changes.

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115