The solubility parameter as a tool in understanding liquid chromatography

The Solubility Parameter as a Tool in Understanding Liquid Chromatography

P. J. S c h o e n m a k e r s * / H . A. H. B i l l i e t / L . de Galan

Laboratorium voor Analytische Scheikunde, Technische Hogeschool Delft, Jaffalaan 9, NL-2628 BX Delft, The Netherlands

Key Words

Solubility parameter Theory of liquid chromatography Retention Selectivity Specific effects

Summary

The solubility parameter concept is briefly discussed. It is then used to explain some of the current features of liquid partition and adsorption chromatography. Various phase systems are discussed on the basis of three charac- teristies: retention, selectivity (the general separation power of a system) and specificity (increased separation power towards certain pairs of solutes); The emergence of two essentially different techniques, the 'normal phase' and 'reversed phase' modes, will appear as a logical consequence of simplified theory. It also becomes ob- vious why 'reversed phase' applications are so much more numerous. Some suggestions are given for the development of new stationary phases and the improvement of existing ones. The usefulness of the solubility parameter concept to predict the solvent strength of mixed eluents in reversed phase liquid chromatography (RPLC) is demonstrated. Some practical rules for the selection and operation of stationary and mobile phase systems are formulated.

Introduction

During the past decade several attempts have been made to describe and predict solute retention in high-performance liquid chromatography. Two general directions can be dis- tinguished. In the empirical approach experimental data are analysed and classified for systematic features in order to derive general retention rules [1-3] . In the absence of a theoretical frame, it is always dangerous to extrapolate to solutes or phase systems not contained in the original data set. The alternative direction is the development of a theoretical description of the separation processes in liquid chromatography.

* Main author.

Examples of the latter approach are the solvophobic theory for reversed-phase liquid chromatography [4, 5] and the solubility parameter model [ 6 -9 ] . Unfortunately, quantitative predictions have been too unreliable to be of practical use. The understandable disappointment seems to obscure the fact that the theoretical predictions are frequently in more than just qualitative agreement with the observations. Therefore such theories can be used to evaluate and compare different phase systems and to formulate proposals for further improvement.

In this paper we shall explore the potential of the solubilty parameter concept for liquid chromatography.

The solubility parameter concept was established back in the thirties by the work of Hildebrand and Scatchard [10]. The original concept covers regular solutions, that is, solutions that do not show an excess entropy effect upon mixing. In practice, regular solutions are rare [10].

On the other hand, the solubility parameter concept possesses some very attractive features, which have tempted various groups of chromatographers to apply the concept outside its limited scope [6-9, 11, 12] : 1. The solubility parameter concept is based on the assump-

tion that the properties of mixtures can be described by the properties of the pure components.

2. The arithmetic expressions involved (regular mixing rule) are relatively simple.

3. The solubility parameter concept relates to compounds rather than to molecules. It is a macroscopic phenomeno- logical approach and as such relates to practical data in a much more convenient way than a molecular statistical approach would. In earlier discussions regarding the applicability of solubility parameter theory to liquid chromatography, attention has been focussed on quantitation. To that end, the model has not proved successful. We feel, however, that the potential of the solubility parameter as an aid in designing a genuine framework for retention behaviour in liquid chromatography have been greatly underestimated. In this paper we will look upon the various parameters that affect retention and selectivity in LC.

It will be shown, that such a discussion can greatly increase our understanding of the liquid chromatographic separation process.

Chromatographia Vol. 15 No. 3, March 1982 Green Pages 205

0009-5893/82/3 0205-10 ~ 02.00/0 �9 1982 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH

The Solubility Parameter Concept

Solub i l i ty Parameter and Polar i ty

The solubility parameter (8) is defined as follows:

where E is the cohesive energy required to transfer one mole of a substance from the ideal gas phase to its liquid state, a quantity that will always be negative; v is the molar volume of the liquid.

We can use the solubility parameter to give a quantitative meaning to the word polarity. Compounds that are usually refered to as non-polar (e.g. n-alkanes) have a low (but non-zero) cohesive energy, leading to a value for 8 around 7 cal u2 cm -3/2 . Polar compounds exhibit much stronger interactions in the liquid state, leading to an increase in 8 up to a maximum value of 25 cal u2 cm -3/2 observed for water. Some further compounds of particular chromatographic interest are listed in Table I. It is clear, that the polarity scale thus defined, agrees with intuition. Attention is drawn to the extreme polarity of water , which has major consequences in liquid chromatography, as will be seen later.

The Regular Mix ing Rule

The connection between the solubility parameter and chromatographic retention parameters is established through the activity coefficient ('},). The formulation is at its most simple, if we define the pure liquid as the standard state, since then a solute has the same standard state in both chromatographic phases. The regular mixing rule describes the activity coefficient of a solute i in a phase f as:

vi (~i - ~ f ) 2 (2) In 7 ~ i : - RT

where the superscripts oo and H refer to infinite dilution o f the solute and to the assumption that the total free energy effect results only from enthalpy differences be. tween the mixture and the pure liquids. If the molar volume Vi, of liquid i is expressed in cm a and the gas constant, R. in cal mo1-1 K -1 the solubility parameter, 8, is expressed i~ cal t/2 cm- 3/2. If SI units are used, 8 is expressed in J~": m -3/2 or Pa 1/2 , where 1 cal u2 cm -3/2 = 2.05 �9 103 Pa u2 .

In the present discussion we will always use the common units of ca] t/2 cm -3/2 for the solubility parameter. For con. venience wel will usually omit these units.

One conclusion that can be drawn from eq. (2) is that a solute in a liquid phase of the same polarity (6 i = 8 f) has an activity coefficient of 1. This is equivalent to a perfect solution following Raoult's law. More important is the pre. diction by eq. (2), that activity coefficients are never smaller than one. This is tantamount to a positive heat of mixing, �9 is, the mixture is energetically less favourable than the combination of the pure constituents separately. This is in contradiction to practice, where mixing can te endothermic and the activity coefficient smaller than one. One answer [13] to this problem is to expand eq. (2)with an entropy term, completely independent of the enthalpy term described by eq. (2). However, we have noted before that such an extension is of limited value in liquid chromatv graphy [14]. It appears that the entropy and enthalpy con. tributions are strongly correlated and that for polar com. pounds much of the entropy effect is already contained in eq. (2). At the end of this paper we shall discuss another possibility for reconciling the observation o f negative ac. tivity coefficients with the solubility parameter concept. For the moment we shall ignore the problem and delete the superscripts H and oo in eq. (2).

Liqu id Chromatograph ic Retent ion

The basic retention parameter in liquid chromatography is the capacity factor, k. It can be expressed as the ratio of

Table I . Selected values of so lub i l i ty parameters (cal 1/2 cm-3 /2 )

So lu t i l i t y parameter

Polar i ty scale 8

2o

~*~_ ____,-- l O -

5 -

o -

~ 1 6

15.85

~ 1 4

13.14

10.68

10.65

9.88

9.57

9 .53

~ 7

~r 5

A lumina "

Methanol

Pyrocarbon

Aceton i t r i le

Methy lene chlor ide

Dioxane

Tet rahydro furan

Toluene

Ethy l acetate

Alkanes

Perf luor inated alkanes

10.8 ' 9.8 [ ? I 11.4 ' 2.5 ' 8 ' i t i

7.2 3.9 0.1- 17.1 5.4 --.

14 small small " small small I - - I

7,3 5.8 0.2 ~ 1 0 ~ 4 I - 1

8.9 4.38 1 0 ~ ~ 4 ~ 1 t - - I I f

8.1 1.2 3.4 small 2.0 --

' 2 ' 1 8.0 3.3 0.3 ' 6. .5 -

8.5 0,8 0.7 8 0 .4 --

7.6 3.6 1.4 3.5 i 1 -

~ 7 O 0 0 0 -

~ 5 0 t 0 0 0 10

206 C h r o m a t o g r a p h i a V o l . 15 No . 3 , M a r c h 1 9 8 2 Green Pages

the activity coefficients of the solute in the two chromatographic phases [14] :

"Yi, m ns ki - 7i ,s nm (3)

where the subscripts m and s refer to the mobile phase and the stationary phase, respectively. The quantity n is the number of moles of each phase in the chromatographic column.

We now take a drastic step by assuming ~that the solubility parameter concept, originally formulated for regular liquid solutions can also be applied to the various phases en- countered in LC (solid adsorbents, chemically bonded phases). This approach has been shown to be useful [8 ,9] . The combination of eqs. (2) and (3) now provides an expression for the capacity factor of solute i in terms of solubility parameters.

Vi Ink i = ~ - ~ (~m + 6 s - 26 i ) (6m -6 s )+ In -nn m �9 (4)

Eq. (2) predicts two ways to obtain small capacity factors and hence rapid analysis. One way is to choose mobile and stationary phases of equal polarity (5 m = 5s), but such a system clearly offers no chromatographic separation, since k i would be equal for all solutes. The alternative is to select the mobile phase and stationary phase in such a way that the sohite has an intermediate polarity, or

1 ~i = 7 ( ~ m +(~s) �9 (5 )

If eq. (5) applies the capacity factor becomes equal to k i = ns/n m and because n J n m will usually be much smaller than 1, retention times are very short. Apart from the fact that eq. (5) can strictly apply to one solute only, the elution is much too rapid to provide good separation. Conse- quently, we can afford to use a mobile phase of slightly different polarity. Even a minor variation of 8m has a large influence, as is clear bY differentiating eq. (4) towards ~i m for a given phase system, where 6s is constant and eq. (5) can be applied

Aki v i ki - RT (6m -- ~s) A~m - (6)

Shlce 6 m --8 s can easily be equal to 10 cat tn cm-3n (Fig. 1) and vi is of the order of 100cm3mo1-1, we find with RT = 600 ca lmoF I

Ak - - ~ 1.5 A ~ m . k

Consequently, even a minor variation in the mobile phase polarity can have a dramatic effect upon the capacity factor. This is a well known observation in chromatographic systems utilizing binary solvents [ 14, 15].

Another conclusion to be drawn from eq. (4) is the increase in retention with molar volume, vi, or with solute size, another familiar observation in liquid chromatographic practice. For higher members of a homologous series, 6i, will be roughly equal. The frequently observed linear increase of In ki with carbon number in a homologous series then follows from eq. (4).

We also note that the relative variation of retention with mobile phase polarity (eq. (6)) increases with solute size. Indeed, if the water content of the mobile phase in reversed phase LC is increased we usually observe diverging retention curves [15], demonstrating that the more retained, larger solute is more susceptible to mobile phase influence than the smaller solute. However, the question of chromatographic separation deserves a more extensive discussion.

Selectivity

From eq. (4) an expression for the relative retention (a) of two solutes with equal molar volumes (vi = v i) is rapidly derived:

2 v i lna j , i = lnkj /ki = ~- - ( r (7)

It shows that the separation between two solutes can be in- fluenced by two factors: (i) the difference in polarity between the two solutes

(6 i - S t ) . The more the two solutes resemble each other, the closer 8j approaches 6i and the more diffi- cult their separation becomes. Strongly differing solutes (St - 5 j >> 0), should be easily separated;

(it) the difference in polarity between the mobile and the stationary phase (~m - ~ s). This factor is independent of the solutes in the sample. We can define the selectivity of the chromatographic phase system as the absolute difference between the polarities of the two phases: 1 6 m - 6 s l . The larger the difference in polarity between the two phasesl the more powerful is the system for the separation of very similar solutes (6j ~6i).

However, we have seen from eq . (4) that an increase of [Srn - 5 s [ not only increases separation power, but also has a dramatic effect on retention, unless we select the two

n- alkylphases silica fluoroalkanesl ~ pyrocarbon l

5 I0 15 20 25

cal I/2. c m "3/2

- - r - - - - \ /--o o__ ,5 ~ O ~ s 2o 2s ai ----

T t t otLoo, t alkanes THF acetonitrile water

Fig. 1

I l lustration of selection of phase systems for LC according to eq.(5). A sample with polar i ty 12.5 (middle scale) can be eluted f rom silica (8 s = 16; top scale) wi th non-polar mobile phase (8 m = 9; bo t tom scale), or wi th polar solvent in reversed-phase system. Shaded areas represent lat i tude wi th respect to possible variation in mobile phase composit ion.


chromatographic phases in such a way that eq. (5) is obey- ed. The implication is illustrated graphically in Fig. 1, where the polarities of stationary phase, solutes and mobile phase are presented on three parallel axes. For any solute a straight line through the point indicating its polarity on the solute scale intersects the two other Scales in two points forming a mobile phase/stationary phase pair satisfying eq. (5).

The two most common stationary phases in HPLC are alkylated silica, with 6 ~ 7, anduncoated silica with a solubility parameter that is probably close to that of alumina: 6 = 16 [8]. I f we now choose a solute of intermediate polarity (~i = 12.5), we find two straight lines connecting on the one hand silica with a low polarity mobile phase (~m =9 ) and on the other hand alkylated silica with a polar eluent (6m = 18). As discussed above, we could allow mobile phases with a polarity slightly different from those calculated from eq. (5). Those are represented by t h e shaded areas in Fig. 1.

The two straight lines in Fig. 1 represent the two well-known separation systems in current HPLC. (i) For a curve with a positive slope in Fig. 1 ,6s > 6m,

and hence it represents a normal or straight phase system. According to eq. (7) a more polar compound (6 i :>6i)wil l be more retained on this system than a less polar one.

(ii) Curves with negative slope in Fig. 1 have 6 s < 6 m and represent reversed phase systems, where the more polar compound will now be retained less and elute more rapidly.

An important observation to be made in Fig. 1 is the difference in slope of the two sets of curves. According to eq.(7), this slope 1 6 m - 6 s l indicates the selectivity of the phase system. The steeper the curve, the less selective the system. For infinite slope (a vertical through 60 we have 6s=6i=gm and the chromatographic phase system shows no selectivity at all. Fig. 1 supports the important conclusion that for all but the highly non-polar compounds a reversed-phase system provides greater selectivity than a normal phase system.

In reality the situation is even more favourable for reversed phase HPLC. I f the solute becomes less polar, the straight line connecting i t with silica soon intersects the mobile phase scale at a point below 6 = 7. in other words, we lack a mobile phase that is sufficiently non-polar to retard low polarity solutes on a normal phase system. On the other hand, solutes that are more polar than the example considered in Fig. 2 can still be separated on a reversed phase syste m, provided we use water as a component of the mobile phase. It is thus the extreme polarity of water (8 = 25) that renders reversed phase HPLC so profitable.

This can also be viewed in another way. With eq. (5) the selectivity of a chromatographic phase system can be expressed in terms of the solute polarity as

~ m - ~ s = 2 ( 6 i - - 6 s ) . (Sa)

I f we now look at a given stationary phase, we see that each solute defines its corresponding mobile phase polarity and selectivity. For example, let us consider a hydrocarbon-type stationary phase with a 6s-value of 7.

For a solute with a polarity of 7, eq. (5a) shows that 6 m should also be 7 and hence file selectivity of the system is zero. Of course, the mobile phase polarity can be taken slightly higher, resulting in a higher selectivity at the cost of larger retention. Although in practice some extra selectivity can be gained in this way, we will consider the results from eq. (5a) as a first approximation.

For a slightly more polar solute, we see that the appro- priate 6m-value and the selectivity increase. Both change twice as rapidly as 6i itself. Therefore we cannot go on for. ever. There is a practical limit to the polarity of the mobile phase. Water, with a 6m-value of 25.5 is the most polar mobile phase available. According to eq. (7) this leads t0a maximum solute polarity of 16.25, where the general selectivity of the system is 18.5.

The selectivity we have found above can be plotted against the polarity of the solute involved. For the reversed phase material discussed above this is done in Fig. 2. The line AT starts at zero selectivity for 6i = 7 and runs up to a selectivity of 18.5 for6 i = 16.25.

A similar argument can be given for other stationary phases. I f we consider alumina (6s = 16), this moderately polar stationary phase can be combined with water for solutes up to ~i = 20.75; alternatively, it can be combined with hexane for solutes starting with ~i = 11.5. For any stationary phag the range in solute polarity is given as

7 +6 s 25.5 + 6 s 2 < 6i "( ~ (8)

This is illustrated in Fig. 2 where we observe - in principle - for each stationary phase two branches. If 6i > 6 s, then als0 6m > 6 s and we are operating in a reversed phase mode This is represented by the branch with positive slope in Fig. 2. I f 6 i < 5s, then also 6 m < 6 s and the branch witha negative slope represents operation in a normal phase mode For extremely non-polar stationary phases only one branch exists (AT in Fig. 2). For more polar stationary phases both branches are feasible, constituting a V-shaped curve touching the axis in 6i =~s, where the selectivity is zero. Note that all branches are con. tained within the triangle ATW!

r

~2c

t Fig. 2

,

Z \ RpFT~ / \

5 A 10 15 20 25 W Solute polarity (~i, call/2.cm-3/2

Calculated select iv i t ies f o r var ious phase systems as function of

solute p o l a r i t y (eq. (5a)).

RPF = per f luo r ina ted reversed-phase; RP = reversed-phase;

PC = py roca rbon ; LSC = a lumina, si l ica.

208 Chromatographia Vol. 15 No. 3, March 1982 Green Pages

Fig.2 shows, that stationary phases with extreme polarity (for example, hydrocarbons) possess potentially a much higher selectivity than stationary phases o f intermediate polarity (for example, alumina). If we compare the line for the liP material to the V-shaped lines for the LSC ad- sorbent, we conclude that the former is superior by far, both with respect to selectivity as to applicability. Remark- ably, the only case for which the LSC system is predicted Io offer improved selectivity, is for polar solutes (6i > 16) in the reversed phase mode. The polar adsorbents should then be operated with water as the mobile phase, to separate very polar solutes (Fig. 2), that cannot be retarded on a non-polar stationary phase.

Evaluation of Stationary Phases

Fig. 2 confirms tile current practice that reversed phase HPLC asing alkylated silica has found much wider application than normal phase HPLC using bare silica. As stated above, the superiority of reversed phase LC systems arises from the extreme polarity of water as the mobile phase. Theoretically, normal phase LC could yield a similar per- f0rmance, if there were a stationary phase with a polarity comparable to water. At present, no such a material is available for LC. However, two other stationary phases have been prepared for HPLC that merit attention on the basis of Fig. 2.

In an attempt to overcome the pH limitations of silica, graphitized carbon black has been suggested by several authors [17-19]. A likely value for the solubility parameter of this material [8] is /5 = 14, if we assume that carbon shows only dispersive interactions [20]. Fig. 2 then readily shows that unmodified carbon can only find limited use in HPLC. The situation would be improved if we could depolarize the carbon stationary phase through chemical modification. Even then carbon would probably not provide better selectivity than alkylated silica, although it would have the advantage of being more chemically inert.

A more interesting proposal is the use of perfluorinated stationary phases [21]. It has been recognized for a long time that perfluorinated hydrocarbons are extremely low polarity compounds. Their polarity is well below that of the alkanes themselves [10]. Using perfluorinated alkanes in liquid chromatography means that we can expand rite triangle AWT in Fig. 2 towards the low polarity end, as is indicated by the thin line. The high cost of perfluorinated alkanes prevents their application as mobile phase. It is, however, fairly simple to synthesize chemically bonded stationary phases containing perfluorinated hydrocarbon chains [21].

Taking a value for 6 of 5 for these phases [i0] we can in- elude their curve in Fig. 2 where we find that a higher selectivity towards low and moderately polar solutes can generally be obtained f rom these extreme low polarity phases.

The retention behaviour observed with perfluorinated stationary phases [21,34] appears to be in agreement with the above predictions. Hence, we conclude that perfluorinated materials lead in general to a higher selectivity.

Fig. 3

Relationship between In k and volume fract ion of three different organic modifiers in binary mixtures wi th water.

�9 Methanol, oE thano l , + n-propanol; solute Phenol; column: LiChrosorb RP-18. Taken f rom ref. [14] (with permission).

!

0

+ -1

.2

0 =.r water a l c o h o l

5! tO

5

The extra cost of the fhiofinated material could well be outweighed by, for example, the use of shorter columns, lower analysis times and decrease in solvent consumption. The substitution of the present hydrocarbon stationary phases by perfluorinated ones seems, therefore, to be an interesting proposition.

Mixed Solvents

Whereas the number of stationary phase in current use in LC is limited, the polarity of the mobile phase can be varied continuously by mixing two or more solvents of different polarity. The solubility parameter of a mixture may be approximated [13] by

~i m = ~ q~p t~p . (9) p

Here ~p and tSp are the volume fractions and solubility parameters of the mixture component p.

By substituting eq. (9) into eq. (4), we can establish the algebraic forms of equations that describe retention behaviour in LC as a function of composition for binary [14] and ternary [22] mixtures. For binary eluents we find:

In k i = A i ~ 2 + Bi~b + C ( 1 0 )

where r is the volume fraction of one of the constituents. In RPLC it is convenient to assign 6 to the volume fraction of the organic modifier that is added to water. The con- stants A, B and C depend on the solubility parameters of the mobile phase components and of the solute. The complete expressions derived from the solubility parameter model show that Bi is strongly negative, whereas Ai is Weakly, but significantly positive. As a result the capacity factor decreases sharply and non linearly with increasing modifier content 4. The most simple equation for Ai is obtained when entropy and phase ratio terms are neglected [14] :

Vi Ai = ~-~ (6w - -~mod) 2 (1 1)

where 6w is the solubility parameter of water and 8mod that of the organic modifier. Hence, a higher curvature of the In k vs 0 curve is expected for less polar organic modifiers. Fig. 3 illustrates the validity of this statement, exploit-

Chrornatographia Vol. 15 No. 3, March 1982 Green Pages 209

ing 3 different organic modifiers on a LiChrosorb RP-18

column with phenol as the solute. The curvature increases systematically in the order

methanol (t~m0d ~ 16) < ethanol (~mod ~- 14) < propanol (t~mo d ~ 12)

The above treatment is readily extended to mixtures of more than two solvents. Instead of a curve relating the capacity factor to the volume fraction of one solvent (Fig. 3), we obtain a multidimensional surface. For the practically interesting case of ternary mixtures, a smooth but non-planar surface is predicted for the variation of retention with mobile phase composition [22]. An example is presented in Fig. 4. The composition of a ternary mobile phase containing THF, methanol and water is represented by the usual equilateral triangle at the bot tom. The logarithm of the capacity factor of o-cresol is plotted vertically. The smooth- ness of the surface in Fig. 4 illustrates the general rule, that ternary" solvents form a gradual transition between the three binary mixtures [22].

Gradient Elution

We have seen that on a given stationary phase, each solute requires a mobile phase of a particular polarity (Fig. 1). For a series of solutes of not too different polarity, a mobile phase can be found that will elute the complete series with roughly optimal k-values. However, if the solutes present in a sample span a wide range in polarity, we can no longer find one mobile phase to serve them all. In this case gradient elution might be an answer to the problem.

onship between In k )mposit ion of ternary tures containing THF ter.

I 10-C 18. 22] (with permission).

In gradient elution we vary the composition (and hence the polarity) of the mobile phase during the analysis. Tiffs prin. ciple is illustrated in Fig. 5. Here we have again drawn three polarity scales, similar to those in Fig. 1. As an example, we discuss the application of a water-methanol gradient in RPLC. If we elute the column with water, we see that solutes with a relatively large polarity (~ > 15) will be elut. ed from the column. However, a solute with a polarity of about 13 leads to a corresponding mobile phase polarity of 19 in Fig. 1 and will hence not be eluted with water. If we now add methanol to the mobile phase, we move to the left along the bot tom scale and we start eluting solutes 0f lower polarity (central axis). I f we continuously add more methanol, we will successively elute solutes of decreasing polarity. As we can see in Fig. 5, the water-methan01 gradient is compatible with solutes varying in polarity be. tween 16 and 11. I f we substitute tetrahydrofuran for methanol , the gradient encompasses all solutes with polar. ities ranging from 16 down to 8. However, for the 10~' polarity solutes the selectivity will be rather poor (Fig. 5).

The Secondary Effect : Specificity

It should be emphasized at this point that the treatment so far has been greatly simplified. The one-dimensional s0lu- bility parameter concept has aided our understanding 0fa variety of phenomena in liquid chromatography in a general way. We have seen how retention is determined by the polarity of the solute with respect to the polarities of the mobile and stationary phases (eq. (4)). The general selectivity of the chromatographic system has been related to the polarity difference of the two phases (eq. (7)). The combination has allowed a comparison of stationary phases and an evaluation of mobile phase effects including gradient elution.

Obviously, however, the molecular interactions in the liquid state are much too complex to be described by a single parameter. The simplified solubility parameter model has itslimitations. We recall that eq. (2) is unable to account for activity coefficients smaller than one. ' Another failure

1

I n k

l ~ - 1

(3)wate l

(2)THF

-2

, -3

,(1) MeOH'

Si RP 10 t5 20 25 ~ , , l ~i s caw I/2 cm-3/2

THF MeOH H20 F i g . 5

Diagram illustrating application of gradient elut ion in RPLC. Arrows indicate that variation in mobile phase polar i ty due to gradual replacement of water by methanol or THF in mobi le phase (bott0m scale) leads to rapid elut ion of solutes clown to polarities 12 and 8, respectively (middle scale).


of the simple treatment is its inability to distinguish such different compounds as ethyl acetate (6 = 9.53) and toluene (6 = 9.57) or methylenechloride (6 = 10.68) and dioxane (~ = 10.65). Clearly, a refinement of the solubility parameter concept is required, if we want to transfer from general rules to specific situations.

Such a refinement is offered by the multieomponent solubility parameter model. This model acknowledges the existence of different types of interactions in the pure liquid. The different types of interaction are assumed to be independent, leading to an additional set of interaction energies. The same assumption is suggested for mixtures. For each individual type of interaction we can now define a separate solubility parameter and apply the regular mixing rule.

Several multiparameter models have been proposed, differing mainly in the number of possible interactions included [6-9, 11, 2 3 - 2 8 ] .

Table II gives a brief review Of the possible types of interaction. It states the parameter assigned to a specific interaction, the physico-chemical data it can be related to and the expression for the interaction energy in the pure liquid and in a mixture. The last three columns in TablelI indicate which interactions occur in mixtures of polar (p) and non- polar (np) compounds. Dispersion interaction arises from the mutual disturbance of the electron clouds of interacting molecules. This type of interaction was quantitatively explained by London [29, 30] and is sometimes refered to as London interaction. Since every molecule has a cloud of electrons, dispersion interactions occur in all mixtures, polar or non-polar. Dipole orientation reflects the energy gain when the negative end of an electric dipole is surrounded by positive ends of similar or other dipoles. Since a permanent dipole moment is required, only polar molecules can participate in this type of interaction.

Dipole induction occurs when a molecule that posesses a permanent dipole moment induces a temporary dipole in a neighbouring molecule, that does not necessarily posess a dipole moment of its own. The fundamentals of both orientation and induction interactions have been quantitatively described by B6ttcher [31 ]. Acid-base interaction covers all the exchanges of electrons and protons (hydrogen ions) between molecules. To obtain

an interaction, both characteristics should be present, that is, a basic function is needed to interact with an acidic function. Hence, all participating molecules should have polar characteristics.

I f we add all the interaction energies we find for the total solubility parameter of a pure liquid (see Table II):

62 = 6~ + 60 z + 26in d 6 d + 26a6 b. (12)

Note that two different kinds of terms appear in eq. (12). Quadratic terms refer to dispersion and orientation, whereas double product terms arise from induction and acid-base interaction. We refer to the first type of interaction as symmetrical and to the latter as non-symmetrical. In a symmetrical interaction, both participating molecules play identical roles, while in a non-symmetrical interaction the molecules participate on different basis.

By analogy with eq. (2), we can now express the activity coefficient in mult icomponent solubility parameters:

V i ln3`i.f = R T { ( 6 d ' i - - 6 d ' f ) 2 + ( 6 ~ 1 7 6 +

2 (6d,i -- 6d,f) (6ind,i -- ~Sind,f) +

2 (6a, i -- ~ia, f ) ( 6b , i -- 6 b , f ) } �9 ( 1 3 )

While eq. (2) always yields positive values for In3, (i.e. 7 > 1) eq. (13) can lead to negative values for In'),. This is quickly understood from the mixture of an acidic solute (large ~a,i) with a basic phase (large ~b,f). The heat of mixing is then correctly predicted to be negative.

It is now also possible, that two solutes with equal total solubility parameters yield quite different activity coefficients. This can readily be seen from the partial polarities listed in Table I. Combination of eq. (13) with eq. (4) and eq. (7) now yields for the relative retention of two solutes with equal molar volumes:

2 v i in O~j, i = RT { ( ~ d , i - - 6 d , j ) (6d,m - - 5 d , s ) +

(6o , i -- a o , j ) (ao, m -- ao , s ) + (ad , i -- 6 d , j ) X

(a ind ,m - - a i n d , s ) + ( a i n d , i - - 6 i n d , j ) ( a d , m - - a d , s ) +

(6a, i - 6a, i) (6b,m - 6b,s) + (6b,i -- 6b,j)

(6a, m -Ba, s)} . (14)

T a b l e II. Review of specific interactions Type of Parameter Related to Interact ion Interact ion type of m ix tu re

interact ion in pure l iquid in mix ture NP/NP NP/P P/P

Dispersion " 8d Refractive index 6d 2 ( 6 d i - 6 d f ) 2 + + +

Or ientat ion - - +

Induct ion

Acid

Base

60

6 ind

6 8

I 6 b

Dipole moment

Dielectr ic

Constant

Enthalpy of acid -base

In teraction

602

26 ind 6d

2~}aa b

(6oi - 6of) 2

2(6di - 6 d f ) x

( 6 i n d i - 6 indf)

2(6ai - ~Saf) x

(6bi - S b f )

- - + 4 -

_ - - +


This rather awkward expression can be reduced to a manage- able format by considering that the relative retention is described as the difference of two internal products of vectors in a five dimensional space (out of the six terms in eq. (14) only five are independent). The five coordinates of the solute vector can be listed as follows:

X 1 = ~d

X2 = ~ o X3 = ~ind X 4 = t ~ a

X5 = t ~ b

The combination of a certain mobile phase with a given stationary phase defines the vector for the phase system with coordinates

Yt = (~d,m +~ind,m)--(~d,s+~ind,s) Y2 = ~o ,m-5o , s Y3 ---- ~ d , m - - ~ d , s

Y4 =~b,m--~b,s Ys = ~a,m -~a,s

and for eq. (14) we can now write

R--T-T In •j, i = ( x i - x j ) " 9 . (15) 2 vi

It has been recognized before [8] that there is a strong resemblance between eq. (15) and the empirical Rohr- schneider classification scheme for gas chromatography. However, the coordinates in the present system are of a much less empirical nature than the Rohrschneider parameters. The significance of eq. (15) becomes clear from partial differentiation, e.g.

RT 1 ~(~j, i 2vi "'aj,i tiYn - - Xn'i--Xn'j (16)

where n denotes the n'th coordinate. Eq. (16) says that the relative change in O~ji arising from a change in the n'th coordinate for the chromatographic system is directly pro- portional to the difference in the n'th parameter of the two solutes. Conversely, the coordinate that differs most between the two solutes is the one that can be exploited best to enhance their separation. Here we have the key to explore specific interactions and specific selectivity.

Separation of Non-Polar Compounds

We have seen before (Table II) that non-polar compounds show only dispersion interaction. Hence, to separate non- polar compounds of similar molar volume we have to rely on the difference in their dispersion parameter, ~i a.

Eq. (16) tells us then, that we should try and maximize the parameter y l . This can be done by increasing the difference in dispersion or induction characteristics of the two chromatographic phases. The latter cannot be done without changing all the other partial polarities and hence changing retention in a way that is usually hard to predict. Dispersion parameters can however be varied quite considerably without significantly changing the other parameters.

A hydrocarbon material has a dispersion parameter of about 7, comparable to that of many common solvents.

The perfluorinated stationary phases discussed before have a dispersion parameter that is only about 5. The introduction of fluorine atoms in a hydrocarbon molecule will decrease its dispersion parameter, Hence, for two molecules that differ only by the presence of a fluorine atom (RH and RF) the coordinate Yl can be increased quite considerably by replacing a hydrocarbon stationary phase by a per. fluorinated material. According to eq. (!6) this will then result in a specific retardation of fluorinated molecules.

Such a phenomenon has indeed been observed in practice [21] and was then refered to as a specific fluorine-fluorine interaction. We see now that the observations can als0 readily be explained in terms of eq. (16).

Another way to influence the dispersion characteristics without influencing other parameters of the stationary phase seems to be the replacement of a hydrocarbon stationary phase by graphitized carbon black (see Table I). This could lead to a large decrease in the value of Yl. Hence, it should be possible to separate the RH and RF compounds also on a pyrocarbon type of material, using a low-dispersive solvent. The stationary phase would then appear to show a specific affinity towards hydrogen in comparison to fluorine.

The observation by Colin et al. [32] and Unger et al. [18] that graphite shows a higher hydrophobic selectivity than conventional hydrocarbon materials can be attributed to the same effect.

Separation of Polar Compounds

For the separation of solutes that differ in polar characteristics (such as dipole moment), but have the same hydro phobicity (the same hydrocarbon skeleton), LSC on silica seems to be a logical choice. Different functional groups can be expected to show different afinities for the silica surface and this will then result in chromatographic separation.

However, eq. (14) suggests that it is the difference in p01a characteristics of the two phases that determines the extent of the separation. Hence, polar solutes can very well be separated on non-polar columns, provided that a polar mobile phase is used. In this light it would be unwise to try and enhance the separation of nitriles, for example, by replacing a hydrocarbon type of stationary phase by a cyano type material. In the presence of a polar mobile phase such an expedient would only reduce the difference in polarity between the stationary and the mobile phase and deteriorate the separation. Doping the mobile phase with an additive with a large dipole moment would be a much better choice, because this would enhance the specific polarity difference with the stationary phase and improve separation.

Exploiting Specific Mobile Phase Effects in RPLC

We have seen that on a given stationary phase each solute defines its own optimum mobile phase polarity. Hence, in RPLC, there is an optimum binary composition for each organi c modifier to realize the same polarity.

212 Chromatographia Vol. 15 No. 3, March 1982 Green Pagss

us consider, for example, two binary eluents, one o f thanol-water and one of THF-water. Equal polarity of two eluents is obtained if (eq. (9)).

~I6M +(1 -- (~M)~W = r + ( 1 -- ~ T ) (~W

~ W - - ~ M _ _ . Or = 6 w - 6 r q~M �9 (17)

is the composition of a THF-water mixture that will ~e the same polarity as a methanol-water mixture of com- siti0n ~M. Hence, the solute retention and the general ectiviW of the two systems will be similar. However, the ,lial polarities of the two mixtures are different (Table I), d hence a specific, effect could occur, resulting in a "ferent chromatogram.

e~i0usly, we have considered this possibility from an .~pifical point of view [33] . t calculated the compositions of acetonitrile-water and ~F-water mixtures empirically from actual chromato- ~phic data for a large number of solutes. The result is an erage volume fraction of acetonitrile and THF that is ex- acted to yield the same retention times as a given volume action of methanol. For different solutes, the correspond-

compositions varied around the average, indicating the 'tsence of a specific effect.

i Fig. 6 we compare the corresponding compositions given r (17), to the previously obtained experimental curves. good agreement between the simple theoretical ex-

'e~i0n and practice is observed. ence, for a given set of solutes a certain composition of tthan01-water can be used, as well as a mixture of aceton- rile-water and one of THF-water. Specific differences can ~adily be shown to occur between the three eluents [33].

tside the possibility of using different binary mixtures, it als0 possible to use ternary mixtures to vary specificity

.~ntinuously, while keeping retention (and general selec- ~ity) roughly constant�9 This can easily be understood

eq. (9). If we mix two binary solvents (A and B) with qual polarity the resulting mixture will have the same 01arity, whatever the ratio of A and B in the mixture. ~., if we take two binary solvents containing 70 % methanol iwater and 55% acetonitrile in water respectively (see ~. 6), any mixture of A and B will have a polarity of 18.8. t~s is illustrated graphically in Fig. 7: In this figure we have 0siti0ned the equilateral triangle representing the ternary b, ase system methanol-acetonitrile-water in such a way ~t the vertices correspond to the polarities of water !5.52), methanol (15.85) and acetonitrile (13.14). This ay, each vertical line within the triangle connects two b.a~, and a series of ternary mixtures of equal polarity.

It can use ternary mixtures to vary specifity continuously ~er a range limited by the binary extremes�9 This is not 0~ible if we restrict ourselves to binary mixtures, and ~refore separations that cannot be achieved using binary ~bile phases can sometimes be realized with a ternary

Fig. 6

Corresponding compositions of binary mobile phases in RPLC. Calculated values from eq. (17), using solubil i ty parameters from Table I. Experimental values f rom ref. [33 I.

1

q~x

1 - - calc, �9 . exp.. ~ /

/

= QM

ACN

I ~ , Water

t MeOH I

I I i ' I I I I 5 ~i s 10 15 18.8 20 25

= Polarity ( i~ ), cal V2. cm-3/2 Fig. 7

Constant polar i ty lines for ternary mobi le phase s y s t e m in RPLC�9 S y s t e m : methanol-acetonitri le-water is represented by conventional equilateral triangle, ver t ices are situated at polarit ies of individual mobile phase components on horizontal scale. Each vertical line illustrates an inf inite number of mixtures, all wi th the same polari ty.

Conclusions

Ill this paper we have demonstrated how the solubility parameter concept can be used to explain many features of present day liquid partition and adsorption chromatography. The total solubility parameter gives a quantitative meaning to the concept of polarity. On this basis the following conclusions can be drawn.

1. Reasonable retention times are obtained, if the polarity of the solute is roughly intermediate between the polarities of the mobile and stationary phase.

2. For higher members of a homologous series, that have approximately the same polarity, the logarithm of the capacity factor varies linearly with the molar volume or the carbon number.

3. The absolute difference in polarity between the mobile phase and the stationary phase can be defined as the general selectivity of an LC-system.

4. There are two principally different ways to elute a given compound with a selective phase system: the normal- phase mode ((5s>(Sm) and the reversed-phase mode (Sm > 6 s ) . Reversed-phase systems offer superior general selectivity. Solutes will be eluted in ascending order of polarity in normal-phase systems and in des- cending order of polartiy in reversed-phase systems.

~r0matographia Vol. 15 No. 3, March 1982 Green Pages 213

5. Although stationary phases of intermediate polarity (alumina, Silica, carbon) provide only moderate general selectivity, they are potentially most powerful for very polar solutes when operated in the reversed-phase mode.

6. Perfluorinated stationary phases should offer superior selectivity in comparison to the current hydrocarbon, bonded-stationary phases.

7. Specific separation effects can be understood from multi- component solubility parameter theory as the difference of two vector products in a five-dimensional space. Specific effects for non-polar compounds are predicted with perfluorinated and graphitized carbon black, stationary phases. Specific selectivity for polar compounds in reversed-phase LC can be realized with polar additives to the mobile phase.

8. Previously formulated transfer rules for binary mobile phases in reversed-phase LC are readily explained by solubility parameter expressions.

References

[1] L.R . Snyder, 1. Chr0matogr. 92, 223 (1974). [2] L.R . Snyder, J. Chrom. Sci. 16,223 (1978). [3] R. McCormick. P. Z Schoenmakers, B. L. Karger, IVth In-

ternational Symposium on Column Liquid Chromatography, Boston, 1979.

[4] C. Horvdth, W. Melander, L Molnltr, J. Chromatogr. 125, 129 (1976).

[5] C. Horvdth, W. Melander, I. Molndr, Anal. Chem. 49, 142 (1977).

[6] R. A. Keller, B. L. Karger, L. R. Snyder, in: "Gas Chroma- tography 1970", R. Stock (Ed.), Institute of Petroleum, London 1971;p. 125.

[7] B. L. Karger, C. Eon, L. R. Snyder, 1. Chromatogr. 125, 71 (1976).

[8] B. L. Karger, L. R. Snyder, C. Eon, Anal. Chem. 50, 2126 (1978).

[9] R. Tijssen, H. A. H. Billiet, P. J. Schoenmakers, J. Chroma- togr. 122,185 (1976).

[10] Z H. Hildebrand, J. M. Prausnitz, R. L. Scott, "Regular and Related Solutions", Van Nostrand Reinhold, New York, 1970.

[11] H.G. Harris, J. M. Prausnitz, J. Chrom. Sci. 7,685 (1969). [12] P. Alessi, L Kikic, G. Torriano, J. Chromatogr. 106, 17

(1975). [13] A . F . M . Barton, Chem. Rev. 75,731 (1975). [14] P. J. Schoenmakers, H. A. H. Billiet, R. Ti]ssen, L. de Galan,

J. Chromatogr. 149,519 (1978). [15] P. J. Schoenmakers, 11. A. H. Billiet, L. de Galan, J. Chr~

matogr. 185,179 (1979). [16] H. Colin, C. Eon, G. Guiochon, J. Chromatogr. 119,41

(1976); ibid. 122,223 (1976). [17] H. Colin, G. Guiochon, J. Chromatogr. 137, 19 (1976). [18] K. K. Unger, P. Roumeliotis, H. Mueller, G. Goetz, J. Chr~

matogr. 202, 3 (1980). [19] E. Smolkovd, J. Zima, F. Dousek, J. Jansta, Z. Plz~k, J.

Chromatogr. 191, 61 (1980). [20] A. V. Kiselev, Discuss. Faraday Soc. 40, 228 (1964). [21] G. E. Berendsen, K. A. Pikaart, L. de Galan, C. Oliernan,

Anal. Chem. 52, 1990 (1980). [22] P. J. Schoenmakers, H. A. H. Billiet, L. de Galan, J. Chr~

matogr. 218,261 (1981). [23] C. Hansen, ,4. Beerbower, in: "Kirk-Othmer encyclopedia

of chemical technology" , 2nd edition, suppl, vol., New York, 1971;p. 889.

[24] J. D. Crowley, G. S. Teague, J. W. Lowe jr,, J. Paint Tech. nol. 38 (496), 269 (1966); 39 (504), 19 (1967).

[25] E. B. Bagley, T. P. Nelson, Z M. Scigliano, J. Paint Tech. nol. 43 (555), 35 (1971).

[26] E. B. Bagley, T.P. Nelson, J. W. Barlow, S.-A. Chen, I. & E. C. Fund. 9, 93 (1970).

[27] E. B. Bagley, T.P. Nelson, S.-A. Chen, J. W. Barlow, I. & E. C. Fund. 10, 27 (1971).

[28] L A. Wiehe, E. B. Bagley, A.I.Ch.E.Journ. 13,836 (1976). [29] F. London, Z. Physik. Chem. BI1,222 (1930). [30] F. London, Trans. Faraday Soc. 33, 8 (1937). [31] C.J .F. Bdttcher, '~l'heory of electric polarization", Elsevier,

Amsterdam, 1952 (1975). [32] H. Colin, N. Ward, G. Guioehon, J. Chromat0gr. 149, 169

(1978). [33] P. J. Schoenmakers, 1t. A. 1t. Billiet, L. de Galan, J. Chro

matogr. 205, 13 (1981). [34] H. A. H. Billiet. P. S. Schoenmakers, L. de'Galan, J. Chre

matogr. 218,443 (1981).

Received: Nov. 24, 1981 Accepted: Nov. 25, 1981 B


The solubility parameter as a tool in understanding liquid chromatography

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