Gas chromatography on a self-associating component of a binary

Gas Chromatography on a Self-Associating Component of a Binary Phase. Retention Model by Formal Analogy with Conductance of Electrolytes in Dilute Solution T. Kowalska I / T. H o b o 2 / K. Watabe 3 / E. Gil-Av .4 1Institute of Chemistry, Silesian University, 40-006 Katowice, Poland 2Department of Industrial Chemistry, Faculty of Technology, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo 192-03, Japan 3Central Research Laboratory, R/D Operations, Shimadju Corporation, Nishinoyo-Kuwabaracho, Nakagyo-ku, Kyoto 604, Japan 4Department of Organic Chemistry, The Weizmann Institute of Science, Rehovot 76100, Israel

can significantly influence solute retention. Analysis of this phenomenon, in terms of the equilibria occurring in multi-component liquid mobile phases, gave rise to a new LC retention model (LC-model, for short) [1-3], which permits prediction of solute retention and optimization of separation. It is of obvious interest to determine whether the approach used for the development of the LC-model can also be applied to GC, though multicomponent stationary phases are much less common in this mode of chromatography.

Key Words Gas chromatography Binary stationary phase Self-associating phase components Retention model

Summary The dependence of specific retention by a binary stationary phase in GC can be expressed as the sum of the products of the specific retention of the pure comPOnents times their respective volume fractions. In this Study, however, one component has a site, which is not Only mainly responsible for the selectivity, but also participates in strong self-association. This requires introduction of a concentration-dependent factor (gx) in the COrresponding term of the equation correlating VgXix with x. In the GC resolution of N-trifluoroacetyl-amino acid isopropyl esters on a binary phase, N-lauroyl-L-valine t-butyl amide-squalane, data for the values of gx Were obtained. Adapting a previously developed LC retention model to the above GC data, an equation was derived for the dePendence of ~x on the weight fraction (x) of the selector, namely ~tx = lq-i-~--x.This relationship permits calculation of retention volumes on the binary phase for a given x, as well as corresponding resolution coefficients of enantiomeric amino acid derivatives with generally excellent agreement with experiment. The chirality of the system is not relevant to application of the equation.

Introduction Irttermolecular interactions through hydrogen bonds in a mobile phase, containing a self-associating solvent, Chrornatographia Vol. 41, No. 3/4, August 1995 0009-5893/95/08 0221-06 $ 03.00/0

Some of the present authors [4--7] have studied binary, GC stationary phases comprising self-associating diamides (scheme 1) and aliphatic hydrocarbon diluents. It was found that retention of hydrogen-bonding, amino acid derivatives (scheme 1) could not be described by Eq. (1), which disregards intermolecular interactions in the solvents, and was successfully used by Purnell and coworkers [8-10] in their systems: VgXix = Vglx + Vg 2 (1 - x)

(1)

where VgXix, Vg 1 and Vg 2 are specific retention volumes of a solute on, respectively, the binary mixture, pure 1 and pure 2 components, and x is the weight fraction of component 1 in the binary system. In contrast, in the system investigated by the present authors, the nonlinear Eq. (2) was introduced [11], which takes into account the shift of association-dissociation equilibria of the diamides, induced by dilution with the hydrocarbon: VgXix = gxVgPx + Vg a (1 - x)

(2)

where p = polar self-associating solvent, a = apolar constituent, and correction factor gx varies with x. The experimental results obtained offer an opportunity to check the application of the above LC-model to GC. The diamide used in our studies was N-lauroyl-L-valine t-butyl amide. It may be noted that in the context of this article, the optical activity of the diamide is an inciden-

Original

9 1995 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH

221

n-MERE DIAMIDE

I '

"

II R ~

InternalH-BondSites

~

iP

'

I II

'

I

H(

~

~

I

I I I

~ ,

SOLUTE

~.

I

R3

I I I

PeripheralH-BondSites

Scheme 1 Parallel pleated sheet 13structure of an c~-aminoacid diamide and interaction of the peripheral hydrogen bonding sites with solute molecules, formingring structures resembling those present in the pleated sheet.

tal feature. Any conclusion reached would also apply to an achiral, self-associating, phase component.

Experimental The experimental values for Vgmix and gx, in the Tables, were measured on 2 m x 1/8" stainless steel or aluminum columns, filled with Chrom G (AW, DMCS, 80-100 mesh), coated with 70-130 mg N-lauroyl-L-valine tbutyl amide-squalane mixtures of various compositions. The columns were conditioned for 1 day at 135 ~ and measurements carried out on a Hewlett-Packard Model 7620 chromatograph provided with an FID; the column was kept at 95 ~ and the carrier gas was He. Solutes studied were the N-trifluoroacetyl isopropyl esters of Ala, Val, Leu, Abu (cx-aminobutyric acid) and Nva (otamino-n-valeric acid). The raw retention data were corrected for the effect of temperature and pressure to obtain the corresponding specific retentions. It may be pointed out that in paper [11], Vg was expressed in ml mg-1 for reasons of convenience; here the conventional units of ml g-1 are used. For further details, see [111.

Correlation o f gx with x In Table I, it can be seen that Ixx increases as x decreases. This result is in keeping with the view that interaction with the diamide increases as it dissociates on dilution into smaller entities which offer more free hydrogen bonding sites to the solute per unit weight. The factor gx is, thus, linked to dilution of the diamide by the squalane. A parallel effect in LC has been interpreted by the above model developed by Kowalska [1-3]. To find the relationship between gx and x in the GC system, the same approach will be used in this paper. The LC-model is based on the formal analogy between the electric conductance of salts in dilute solution and 222

the contribution to chromatographic retention of a selfassociating phase component [see Eq. (2)]. In both cases, the entities formed on dissociation are the seat of the phenomenon concerned. For the electrical conduCtance of salts, Ostwald's dilution law defines the degree of dissociation ([3) of the electrolyte by: 13 = ~ / K / c

(3)

where K = dissociation constant and c = molar concentration (before dissociation) of the salt. The equation is strictly speaking valid for dilute solutions only. The electrical conductance of salts in solutions is proportional to their degree of dissociation. Ostwald's dilution law can also be applied to the disso" clarion of self-associating solvents. In this case, the equilibrium of association-dissociation is, however, not represented by an equation of the type [AB]_ - [A] + [B] but by a complex series of reactions: [n-mer] ~ [(n-1)mer] + [monomer]; [ ( n - 1 ) m e r ] ~ [(n-2)mer] +[monomer] etc.

(4)

where n, (n-l), (n-2), etc. denote the numbers of solvent molecules (monomers) associated. Eq. (4) calls for a redefinition of K and c in Eq. (3). It is generally assumed that the complex equilibria in Eq. (4) can be approximately represented by: K' [n'-mer] _ ,. [(n'-l)mer] + [monomer]

(5).

where n' = hypothetical average degree of association and K' = corresponding equilibrium constant. It is, thus, necessary to replace K and c in Ostwald's dilution law by the above hypothetical parameters, i.e.:

= qK'/c

,

(39

where cx, is the molar concentration of the hypothetical n'-mer at weight fraction x, before dissociation in accordance with Eq. (5).

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While K' and c x, are unknown, their ratio can be derived from the specific retention on the pure diamide. As in the case of electrical conductance, it is assumed that the contribution to retention of the selfassociating solvent is proportional to the degree of dissociation. To calculate the contribution of the self-associating solvent [lax VgP (x)] to the overall retention (Eq. 2), [3 has to be multiplied by a proportionality constant Cp: laxVgPx = Cp~x = Cp "4 K ' / e x, x

For the present system the densities are dp = 0.905 g m1-1 for the diamide and da = 0.757 g m -1 for squalane at the temperature of the experiments (95 ~ One can, thus, write: lax = ~/1/qbx = q(1.196 - 0.196x) / x

Results and Discussion

(6)

As mentioned above, a number of approximations were made in the development of Eq. (10). Ostwald's dilution law, strictly speaking valid for dilute solutions only, was used at higher concentrations. Presenting the equilibria in the self-associating solvent by Eq. (4) is also an approximation. Furthermore, in the electrical conductance of salts, the undissociated electrolyte does not participate in the phenomenon. In contrast, the associated structure of the self-associating solvent still contains functional groups free to interact with the solute, as in Scheme 1. In applying, nevertheless, the model to chromatography, the assumption is made that the contribution of the associated structure (Eq. 5) to retention per unit weigh is negligible, as compared with that of the monomer (i.e. n -1 of the latter; a small fraction, when n is large).

To find the value of ~/K'/c x, , it is to be pointed out that the pure solvent (where x = 1) is also in a state of equilibrium according to Eqs. (4) and (5). The constant K' in the pure diamide is thought to be little changed on dilution with apolar hydrocarbon. This assumption can be justified by the expected clustering of polar self-associating component in the apolar squalane. Thus, one can write for the specific retention: VgP = Cp '4 K / c x,

(7)

Where cXn, represents the number of moles in terms of the hypothetical associate of degree n' (before dissociation), contained in 1 g diamide. To define the molar concentration (c x') of the average associate at weight fraction x, c~, has simply to be multiplied by the volume fraction (0 x) of the polar solvent at its weight fraction x in the binary mixture: cX, = r

Correction Factor (~x) A good fit of the experimental values of lax with those predicted by Eq. (10) is the essential test for the applicability of the approach used. The figures given in Table I show that for x = 0.675 and x = 0.25 the experimental mean values of gx are identical with those calculated by Eq. (10), while for x = 0.35 the deviation is no more than 8 %. Thus, the model, despite its above-mentioned flaws, works very well in the binary system studied. Eq. (10) takes into account the difference in the densities of the two phase components. Relevant data on the specific gravities are, however, most often not readily available. Therefore, Eq. (11), in which it is

(8)

By combining Eqs. (6-8), we get: btx VgPx=Cp ~ / K / c x, x = VgP "4 1/r x x and it follows that: lax = ~/1 / Cx

(10)

(9)

Finally, qb can be expressed in terms of x, when the Specific densities of the components at the temperature at which the experiments were carried out are known, and on the assumption that no volume change of comPonents occurs on mixing. The corresponding equation

~x = "4 1/x

(11)

is:

assumed that dp / da 9 1, was also used for the calculation of I.tx. Except for x = 0.35, the results (Table I, last

Cx= x / [x + (1 - x) d p / da]

Table I. Correction factors (px) for N-lauroyl-L-valine-t-butyl amide-squalane and N-trifluoroacetyl-a-amino acid isopropyl ester solutes. Comparison of experimental data (la~xp)and values calculated (g~alc)by Eqs. (10) and (11). X

I-tXexpof N-TFA amino acid iopropyl esters of : L-AIa

D-AIa

L-Abu a D-Abu a L-Nva b D-Nva b

L-Val

Mean value c

D-Val

L-Leu

D-Leu

I~ale ~alc Eq. (10) Eq. (11)

1.000

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.00

1.00

1.00

0.675 0.350 0.250

1.2 1.8 1.9

1.2 1.8 1.8

1.3 2.1 2.3

1.3 2.1 2.3

1.3 2.1 2.3

1.3 2.1 2.3

1.2 1.9 2.0

1.2 1,9 1.9

1.3 1.9 2.2

13 1.9 2.1

1.26 (+ 0.016) 1.96 (+ 0.06) 2.11 (+ 0.06)

1.26 1.80 2.14

1.22 1.69 2.00

%t-aminobutyricacid. ba-amino-n-valericacid. CMeanerror on all observations in parenthesis.

Chromatographia Vol. 41, No. 3/4, August 1995

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223

column) did not differ significantly from those calculated with Eq. (10), even though for the system diamidesqualane the difference in density of the two phase components is 20 %. This indicates that the simpler and more convenient Eq. (11) can be used instead of the strictly more accurate Eq. (10), so that, in general, no knowledge of the respective densities will be required. The practical usefulness of Eq. (11) is further elaborated below.

Specific Retention Volumes (VgXmix) Once gx is known, VgXmix can be readily obtained by Eq. (2) (see Table II). The necessary specific retention data on pure phase components, VgP and Vg a, appear, respectively, in the rows for x = 1.0 and x = 0.0 of the Table. These calculations show that the results, except in one case, were lower than the experimental data. Out of 30 VgXmix values calculated, 21 showed deviations from experiment of only 1-5 % whereas of the other

Table II. Experimental and calculated values of specific retention voluumes (VgXmix)for diamide-squalane.

LVgXmixml g-1 Compound

+

exp.1

calc.2 (% error) 3

x

exp)

1.00 0.675 0.35 0.25 0.00

794 720 666 549 235

794 749(+ 3.9) 652 (-2.1) 602 (+ 9.7) 235

605 605 558 589(+ 5.6) 540 533 (- 1.3) 454 500 (+ 10.1) 235 235

Val

1.00 0.675 0.35 0.25 0.00

1318 1235 1247 1084 589

1318 1308(+5.9) 1210(-2.9) 1147 (+ 5.8) 589

1021 998 1060 934 589

1021 1056(+.58) 1024(-3.4) 988 (+ 5.8) 589

Leu

1.00 0.675 0.35 0.25 0.00

3620 3558 3080 2738 1006

3620 3395 (-4.6) 2926 (-5.0) 2693 (+ 1.6) 1006

2483 2444 2330 2040 1006

2483 2431 (-0.5) 2213 (-0.7) 2084 (+ 2.2) 1006

Abu

1161 0.675 1139 0.35 1111 0.25 965 0.00 410

1161 1118 (-1.8) 996 (- 10.4) 929 (-3.7) 410

861 873 886 795 410

861 863(-1.1) 800 (-9.7) 768 (- 3.4) 410

Nva

1.00 0.675 0.35 0.25 0.00

2207 2105 (-3.4) 1850(- 12.0) 1729 (- 5.2) 716

1600 1613 1649 1452 716

1600 1591 (- 1.4) 1470(- 1.3) 1394(- 4.0) 716

Ala

1.00

2207 2178 2102 1823 716

calc.2 (% error) 3

DvgXnox ml g-~

1See experimental. 2Calculated by Eqs. (2) and (10), where difference of density of phase components taken into account, i.e.l.tx= ~ 1.196 - 0.196 x X 3

224

nine, only two showed an error > 10 %, namely 1112 %. Thus, the agreement is reasonable, particularly taking into account that there is an uncertainty of about 1-2 % on the chromatographic measurements. The most interesting information to be deduced from the VgXmix data, are the selectivity coefficients (co) of the enantiomers of the amino acid derivatives. As shown below, the estimation of these latter parame" ters is practically unaffected by the errors involved in calculating VgXmix. This is correct, even when using Eq. (11) for estimating gx, which might involve an additional error of about 3--4 %; in the range of the binary phase compositions studied.

Selectivity Coefficients (~) The calculated VgXmix for the pairs of enantiomers of the amino acid derivatives (Table II) served to derive the respective selectivity coefficients. In Table III, the results (acalc) obtained using Eq. (10) for determining gx are in column 4, and those (O(calc), corresponding to use of Eq. (11), appear in columns (5-7). Despite the difference (Table II) for the VgXmix values, correspond" ing to these two equations, the results for Cs to O(calr are very close and to OCexp. It has already been mentioned that Eq. (11) is more convenient to use in practice, and therefore, also the deviation from experimental selectivity coefficients has been given for this case. In column 6, it is seen that the error (% OCexp)is, in general, no more than 2.0 % and only in two cases amounted to as much as 4.2 %. As the free energy of separation of the enantiomers is of interest for structural correlations, the deviation of calculated and experimental AAG values are also listed (column 7). Since AAG is proportional to lncc, the deviations of AAG'calc from AAGexp, are amplified, compared with those of O(calc (column 6). Even so, the error is only in 4 cases: 7-10 %, and 2 cases: 11-15 %.

Selectivity Coefficients at x = 0.076 In the introduction, it is stated that Ostwald's dilution law is strictly speaking limited to small concentrations. It follows that for low x values agreement between experimental and calculated data should be at least as good, if not better, than in the range of phase compositions discussed above. No systematic studies on binary phases with x < 0.25 have been made thus far. Some measurements of resolution coefficients for x = 0.076 are, however, available, and are compared with calculated values in Table IV. The results obtained confirm expectations. Thus, it carl be concluded that, using Eq. (11) [or Eq. (10)], one can predict gx, VgXmix and co, over practically the whole range of composition of the binary phase, if VgP and Vg a are known.

Chromatographia Vol. 41, No. 3/4, August 1995

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Table IIL Resolution of enantiomers of N-trifluoroacetyl-amino acid isopropyl esters on diamide-squalane binary phase. Experimental and calculated resolution factors (cQ. N-TFA amino acid isopropyl esters of

x

Ala

otexp3

Calculated Eq. (10) 1 r

Calculated Eq. (11) 2 O(~atc.

% error of (g,catc.4

% error of AAOcalc.5

1.00 0.675 0.35 0.25 0.00

1.314 1.289 1.233 1.209 1.000

1.314 1.272 1.223 1.203 1.000

1.314 1.272 1.220 1.198 1.000

0.00 - 1.32 - 1.05 - 0.91

0.0 + 5.1 + 4.8 + 4.7

0,00

0.0

Val

1.00 0.675 0.35 0.25 0.00

1.291 1.238 1.176 1.161 1.000

1.291 1.239 1.181 1.161 1.000

1.291 1.237 1.178 1.156 1.000

0.00 - 0.08 + 0.17 - 0.43 0.00

0.0 + 0.5 - 1.1 + 2.7 0.0

Leu

1.00 0.675 0.35 0.25

1.458 1.456 1.322 1.342

1.458 1.397 1.322 1.292

1.000

1.000

0.00 - 4.19 - 0.38 - 4.25 0.00

0.0 + 11.4 + 1.4 + 14.6

0.00

1.458 1.395 1.317 1.285 1.000

1.00 0.675 0.35 0.25

1.349 1.305 1.254 1.214

1.349 1.296 1.245 1.209

1.349 1.294 1.229 1.204

0.00 - 0.84 - 1.99 - 0.82

0.0 + 3.0 + 8.9 + 4.1

0.00

1.000

1.000

1.000

0.00

0.0

1.130 0.675 0.35 0.25 0.130

1.379 1.350 1.275 1.256 1.000

1.379 1.323 1.265 1.240 1.000

1.379 1.322 1.254 1.227 1.006

0.00 - 2.07 - 1.65 - 2.31 0.00

0.0 + 7.0 + 7.0 + 10.9 0.0

Abu

Nva

0.0

ll.tx=~ -- 1.196 - 0.196 x X

2~tx= ~ - 11 ' x ~See Experimental. 4See Table II, footnote 3~ "~ -AAGexp + AAG'caIc9 100 = !n~calr - l n ~ x ~ . % error =

Table IV. Resolution factors of N-trifluoroacetyl-amino acid derivatives on diamide-squalane phase of x = 0.076.

N-TFA O-isopropyl ester of:

~xpa

O~, calc.2

Ala Val Leu Abu Nva

1.12 1.07 1.16 1.10 1.13

1.14 1.10 1.19 1.13 1.15

%

i

See ref [11]. Calculated using Eq. (11). % error = ~ ' c a l c . -- I~exp. O~exp.

100.

- ln0texp

- AAGexp

100.

error of ~ , talc.3

1.8 2.8 2.6 2.7 1.8

Conclusions T h e c o r r e c t i o n f a c t o r (px) has b e e n c o r r e l a t e d w i t h bin a r y p h a s e c o m p o s i t i o n (x) b y Eq. (11) [~tx = ' ~ x ] , using, as for t h e p r e v i o u s l y d e v e l o p e d L C m o d e l , a n a l o g o u s e q u a t i o n s to t h o s e d e s c r i b i n g t h e e l e c t r i c a l c o n d u c t a n c e o f salts in d i l u t e s o l u t i o n . I n d e r i v i n g E q . (11), a n u m b e r of assumptions were made, including putting the ratio of t h e d e n s i t i e s o f t h e p h a s e c o m p o n e n t s c l o s e to o n e (dp/da 9 1.0). D e s p i t e t h e a p p r o x i m a t i o n s i n v o l v e d , E q . (11) t u r n e d o u t to p e r m i t c a l c u l a t i o n o f t h e r e t e n t i o n v o l u m e s (WgXmix) a n d t h e c o r r e s p o n d i n g r e s o l u t i o n f a c t o r s (or for e n a n t i o m e r i c a m i n o a c i d d e r i v a t i v e s , c h r o m a t o graphed, with generally good agreement with experim e n t a l values. E v i d e n c e has b e e n p r o d u c e d t h a t E q . (11) is v a l i d for t h e w h o l e r a n g e of p o s s i b l e p h a s e c o m p o s i t i o n s . T h e

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e q u a t i o n s d e r i v e d should also a p p l y to achiral systems, to self-associating p h a s e c o m p o n e n t s o t h e r than diam i d e s and solutes o t h e r t h a n a m i n o acid derivatives.

References [1] T. Kowalska, Chromatographia 27, 628 (1989). [2] T. Kowalska, J. Planar, Chromatogr. 2, 44 (1989). [3] T. Kowalska, J. High Resolut. Chromatgr. Commun. 12, 474 (1989). [4] T. Hobo, S. Suzuki, K. Watabe, E. Gil-Av, Anal. Chem. 57, 362 (1985). [5] K. Watabe, E. Gil-Av, T. Hobo, S. Suzuki, Part III, Abstracts, 33rd Meeting of the Japan Soc. Anal. Chem. Oct. 1984; Abstracts, p. 535.

226

[6] K. Watabe, E. Gil-Av, T. Hobo, S. Suzuki, Part III, Abstracts, 33rd Meeting of the Japan Soc. Anal. Chem. Oct. 1984; Abstracts, p. 536. [7] T. Horinouchi, T. Hobo, K. Watabe, S. Suzuki, E. Gil-Av, 34th Meeting of the Japan Soc. Anal. Chem. Oct. 1985; Abstracts, p. 619. [8] R.J. Laub, J. H. Purnell, J. Chromatogr. 112, 71 (1975). [9] J. H. Purnell, J. H. Vargas de Andrades, J. Am. Chem. Soc. 97, 3585 (1975). [10] R.J. Laub, J. H. Purnell, J. Am. Chem. Soc. 98, 35 (1976). [11] K. Watabe, E. Gil-Av, T. Hobo, S. Suzuki, Anal. Chem. 61, 1216 (1989).

Chromatographia Vol. 41, No. 3/4, August 1995

Received: Dec 15, 1994 Revised manuscript received: May 31, 1995 Accepted: Jun 6, 1995

Original