Anal. Chem. 1989, 67, 1109-1112
1109
Theory for System Peaks in Ion Pair Chromatography and Its Application to Indirect Detection Jan Stahlberg* Astra Pharmaceutical Production AB, Quality Control, S-151 85 Sodertulje, Sweden
Mats Almgren Institute of Physical Chemistry, University of Uppsala, P.O. Box 532, S-751 21 Uppsala, Sweden
A theory for system peaks and the indirect detection technique in Ion pair chromatography is developed. The theory is based on the electrostatic theory for ion pair chromatography In combination with the mathematical treatment of multicomponent chromatography. Equations are derived for the direction as well as the magnitude of the analyte peaks. The developed theory is used to explain the typical response pattern and response magnitude that are obtained in the Indirect detectlon technique. The developed theory is found to agree with experimental data in the literature.
INTRODUCTION A sample injected into the mobile phase frequently gives a chromatogram with more peaks than the number of analytes in the sample. These peaks always occur when the mobile phase contains more than one component, but the detection of them depends on the detector used. A number of different names have been given to these “extra” peaks; in this paper we will call them system peaks. The general theory for system peaks is well-known, since it results from the mathematical treatment of multicomponent chromatography described by De Vault ( I ) . The theory has been elaborated in a book by Helfferich and Klein (2) and also by Riedo and Kovats (3). The theory for multicomponent chromatography was recently reviewed by Helfferich (4). The chromatographic column is in a state of equilibrium when the mobile-phase components are distributed between the stationary and mobile phase so that the composition of the mobile phase entering the column is identical with the composition of the mobile phase leaving the column. When this equilibrium is perturbed, e.g. when a sample zone is injected, the components in the zone come to a new equilibrium; i.e. the composition of the mobile phase that moves together with the sample zone differs from the original composition. The effect is a net change in the composition of the mobile-phase components in the sample zone. The resulting excess or deficit of the mobile-phase components outside the sample zone moves along the column with the velocity that is characteristic for that component. These peaks are the system peaks. Various aspects of system peaks have been investigated and discussed (5-16). From the above it is clear that the system peak provides information concerning the solvation processes in the column. This approach has been used by Horvath et al. (7),by McCormick and Karger (8), and by Levin and Grushka (12,13)to gain information on the solvation of analytes in the mobile and stationary phases. Another approach is to add a detectable component to the mobile phase and use its concentration change in the sample zone as a means of detection and quantitation of analytes without inherent detectable properties. Several investigators have studied this indirect detection technique in reversed-phase systems by 0003-2700/89/036 1- 1 iO9$0 1.50/0
using uncharged (11, 18, 19) and ionic detectable probe molecules (9, 15-1 7). Methods for simulation of chromatograms obtained by the indirect detection technique have also been studied (10,11, 14). A theory for indirect detection in ion pair chromatography has previously been developed (15). However, this theory is a stoichiometric theory based on the assumption that the analyte and the amphiphilic ions form an ion pair on the stationary phase. In order to formulate a theory for system peaks and indirect detection, expressions are needed for the isotherm of the charged amphiphile as well as for how this isotherm is affected by the analyte. In this paper the concepts developed in the electrostatic theory for ion pair chromatography are used to establish the necessary relations. When this theory is used, the isotherm of the amphiphile is assumed to follow a surface potential modified Langmuir isotherm (see eq 1). This isotherm is in turn based on the following assumptions: (1)The “chemical” part of the free energy of adsorption of the amphiphile to the stationary phase, AGA’, is constant and independent of its concentration in the mobile phase. This means that the amphiphile may not be involved in association processes (e.g. micellization, ion pairing) in the mobile phase. This type of concentration-dependent process may occur when large hydrophobic ions are present in the mobile phase. (2) The adsorbed amphiphile creates an electrostatic surface potential, ici0. The magnitude of the electrostatic interaction should be independent of type of amphiphile and analyte ion; i.e. ion correlation effects in the adsorbed state are neglected. (3) There is a competition between the amphiphilic ions for the limited surface area available. There is also a competition between the analyte ions and the amphiphile leading to a mixed Langmuir isotherm (eq 4). (4) For the adsorption of the analyte ion it is assumed that the “chemical” part of the free energy of adsorption to the stationary phase, AGBo,is constant and independent of amphiphile concentration. It has been found experimentally that these assumptions are fulfilled in a number of typical ion pair chromatographic systems (21-24). It is therefore particularly convenient to develop a theory for system peaks and indirect detection for ion pair chromatography.
THEORY Consider a chromatographic column equilibrated with a mobile phase containing an amphiphilic ion A. The amphiphile is distributed between the stationary and mobile phases, and the equilibrium concentrations are nAO (mol/m2) and CAO (mol/dm3), respectively. The amphiphile adsorbed a t the surface of the stationary phase creates an electrostatic surface potential q0 (V). The surface potential is set to zero when the stationary phase is equilibrated with the mobile phase and cAo = 0. The pore volume of the column per unit length is uo (dm3),and the surface area of the stationary phase per unit length is A. (m2). 1989 American Chemical Society
1110
ANALYTICAL CHEMISTRY, VOL. 61, NO. IO, MAY 15, 1989
(E$* (a),,, ( =
+
(2)c*
:)cA,cB
-
From eq 4 eq 6-9 are obtained, and since CB is assumed to be small, they are given in the limit cB 0. n&ACAe-ZAF*dRTK
(1
B
e-zBFWRT
+ KACAe-ZAF*o/RT)2
(6)
$o is a function of nA and nB; i.e.
By combination of eq 5-8 the following expression is obtained Figure 1. Schematic representation of a small part of the column containing the front of the moving square pulse of B.
A charged analyte ion, B, of low concentration in the mobile phase, is injected at the top of the column. For simplicity the injected pulse is assumed to be square and to retain its shape as it moves along the column; i.e. the equilibrium between the phases is assumed instantaneous and lateral diffusion neglected. When B enters the column, it perturbs the equilibrium distribution of A between the mobile and stationary phase, and a new equilibrium is obtained. This new equilibrium composition for A moves along the column with the same speed as B in what Helfferich calls a coherent state (4). Let us first consider the equilibrium distribution of A between the mobile and stationary phase in absence and presence of B. I t has been shown that the adsorption isotherm for an amphiphile is well represented by a surface potential modified Langmuir isotherm (22,23). When B is absent the expression for the adsorption isotherm is n&ACAOe-ZAF$O/RT (1) *A0 = (1
acB
cd
where
According to the concept of the electrostatic theory for ion pair chromatography we have KBe-ZB%/RT
= k 'B/nop
(11)
which gives
+ KACAOe-2AFJ.o~RT)
where KA = exp(-AGA"/RT) and AGA" is the free energy of adsorption of A onto the stationary phase. nois the monolayer capacity for A on the stationary phase, and t Ais the charge of A. In the presence of B a slightly different surface concentration of A, nA, will ensue. A Taylor expansion of nA around the original point, nAO,in the two variables cA and cB gives
nA - nAO= An, =
( 5 )=
(
+
(
(2)
Since the concentration of B is small, only first-order terms in the expansion are taken into account. The definition of the capacity factor for A in the region of a nonlinear isotherm is
Insertion of eq 3 and 12 in eq 2 gives an expression for the perturbance of the surface concentration of A caused by the presence of B. As reported in the paper by de Vault ( I ) a mass balance is used to calculate the conditions a t the moving boundary. In Figure 1 is shown a small part of the column limited by sections 1 and 2 and containing the front of the square pulse. The front moves a distance Ax when a volume A V is added to the column. The amount of A passing through section 1 is then cAAV, and the amount that passes through section 2 is cA0AV. The amount of A between the sections increases according to the relation [(CA - CAO)
VO
+ (nA
- nA0)AOlAx
A mass balance for A gives the following relation: where p is the phase ratio of the column. With B present in the system the surface concentration of A, nA, is a function of cA, cB, and and assumed to follow to the equation for a surface potential modified mixed Langmuir isotherm, i.e. n&ACAe-ZAFJ'O/RT
nA =
(1
+ KAcAe-zAF*Q/RT + KBcBe-zfl*o/Rq
The rules for partial differentiation give that
(4)
(CA
- CAO)AV =
[(CA
- CAO)VO ( n -~n~o)AolAx
(13)
A mass balance applied to B gives CBAV =
[CgVo
+ n~Ao]Ax
(14)
The boundary moves with the same speed for A and for B; i.e. A V / h is equal in eq 13 and 14, respectively. 1 AV \To
Ax
- I +
( n -~~ A O _ Ao ) nB AO -- 1 + (c.4 - CAO) V O CB V O
(15)
ANALYTICAL CHEMISTRY, VOL. 61, NO. 10, MAY 15, 1989
Since the concentration of B is assumed to be small, its adsorption isotherm is approximately linear; i.e. nB _ - - An, =-
k’B
ACB
(0
CB
(nA-
nA0)
(16)
( C A - CAO)
ACA
kk >
(d$O/anB)
k ’B. Only when the sign of Z A and zB is opposite does the sign of the bracket in the numerator depend on the relative magnitude of the terms in the bracket. In a typical ion pair chromatographic experiment (zAF/RT) (d$o/dnB)ca is of order 4 X lo6 m2/mol and l / n o about 3 X lo5 m2/mol. The sign of the numerator is therefore usually negative. The theoretically obtained response pattern is summarized in Table I and is seen to be the same as that found empirically. However, according to the presented theory deviations from this pattern may be found at high surface charge densities and high ionic strengths, i.e. when
L>9(3) no
RT
anB
cA
It has also been found empirically that the detection sensitivity changes with the retention of the analyte relative to the system peak. It has a maximum when the capacity ratios of the two peaks are the same. The relative response is given by eq 19, or when l / n o is neglected, the following approximation is obtained:
where
K2 =
KIF (alJ.ol/an~)c~
RT( 1 +
%
(m),)
In Figures 2 and 3 experimental data from ref 15 are plotted according to eq 22, and it is seen that the theory agrees with the experimental results. The exact equation, eq 19, predicts that the slope may be steeper when A and B are of the same sign of charge than when they have opposite sign. The physical reason is a competition between A and B ions for the limited number of surface sites. It is estimated above that in normal ion pair chromatographic systems, the competition
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Anal. Chem. 1989, 67. 1112-1117 0,512
1 2 3 4 5 6
Hexanesulfonate Octanesultanate DI-Isopropylamine Triethylamine Hexylamine Trlpropylamlne
Figure 3. Test of the equation for relative response (eq 22). A is naphthalene-2-sulfonate: the analytes used are numbered in the figure. The data are taken from ref 15.
for site contributes to about 10% of the relative response. It is interesting to note that the relative response for uncharged analytes amounts to about 10% of the response for charged analytes (15). More elaborate studies are needed to quantitatively test all predictions made in the presented theory.
LITERATURE CITED (1) De Vault, D. J , Am. Chem. SOC. 1943, 65, 532. (2) Helfferich, F.; Klein, G. Multicomponent Chromatography; Marcel Dekker: New York, 1970. (3) Riedo, F.; Kovats, E. J . Chromatogr. 1982, 239, 1 (4) Helfferich, F. J . Chromatogr. 1986, 373, 45. (5) Mangelsdorf, P. C., Jr. Anal. Chem. 1968, 38. 1540. (6) Melander, W. R.; Erard, J. F.; Horvath, Cs. J . Chromatcgr. 1963, 282, 211. (7) Melander. W.R.: Erard, J. F.: Horvath, Cs. J . Chromatogr. 1983, 282, 229. (8) McCormick, R. M.; Karger, E. L. J . Chromatogr. 1980, 199, 259. (9) Bidlingmeyer, B. A,; Warren, F. V., Jr. Anal. Chem. 1982, 5 4 , 2351. (10) Stranahan, J. J.; Deming. S. N. Anal. Chem. 1982, 54, 1540. (11) Vigh, G.; Leitold, A. J . Chromatogr. 1984. 312, 345. (12) Levin, S.; Grushka. E. Anal. Chem. 1988, 58, 1602. (13) Levin, S.;Grushka, E. Anal. Chem. 1987, 59, 1157. (14) Takeuchi, T.; Watanabe, S.; Murase, K.; Ishii, D. Chromatographia 1988, 2 5 , 107. (15) Cromrnen, J.; Schill. G.; Westerlund, D.; Hackzell, L. Chromatographia 1987, 2 4 , 252. (16) Denkert, M.; Hackzell, L.; Schill, G.; Sjogren, E. J . Chromatogr. 1981, 218, 31. (17) Hackzell. L.; Schill, G. Chromatographia 1982, 15, 437. (18) Hern6, P.; Rensen, M.; Crommen, J. Chromatographia 1984, 79, 274. (19) Perkin, J. E. J . Chromatogr. 1984, 287, 457. ( 2 0 ) Stihlberg, J. J . Chromatogr. 1988, 356, 231. (21) Stlhlberg, J.; Furangen, A. Chromatographia 1987, 2 4 , 783. (22) Stihlberg, J.; Bartha, A. J . Chromatogr. 1988, 456, 253. (23) Stahlberg, J.; Hagglund, I. Anal. Chem. 1988, 6 0 , 1958. (24) Stihlberg, J. Chromatographia 1987, 2 4 , 820.
RECEIVED for review October 19, 1988. Accepted January 31, 1989.
Calcium Chabazite Adsorbent for the Gas Chromatographic Separation of Trace Argon-Oxygen Mixtures Peter J. Maroulis* and Charles G. Coe Air Products and Chemicals, Inc., Allentown, Pennsylvania 18195
Calcium chabazite used as a gas chromatographic packing provides a practical means for analyzlng trace levels of a variety of permanent gases Including oxygen and argon. An outstandlng feature of properly activated calcium chabazlte is its ablllty to resolve argon and oxygen at temperatures above 343 K. The level of dehydration achieved for thls adsorbent has a direct Influence on its efficlency and ability to resolve Ar and 02. I n addition, we found that treating the chabazlte at elevated temperature in an oxidizing atmosphere improves the resolution and lowers the detectability limits for determlnlng oxygen. Part-per-bllllon levels of Ne, Ar, O,, N,, CH4, and CO could be measured by udng a calcium chabazlte column, in comblnatlon with a helium ionization detector. The column efflclency and resolution of this adsorbent were measured as a function of corrected flow rate and column temperature for AI-0, mixtures. Trace Ar and 0, were base-llne-resolved in under 2 min by using a 6-ft column of this adsorbent at 343 K. Thus, calclum chabazite provides a practical adsorbent for analyzing a wide variety of gases wlth conventional Instrumentation.
INTRODUCTION The chromatographic performance of a zeolitic adsorbent depends on many properties, including the particular structure 0003-2700/89/0361-1112$01.50/0
and composition of the zeolite. The number, type, position, and hydration state of the charge-compensating cation present in a zeolite strongly influence its selective adsorption and separation properties ( I ) . As a direct result of fundamental studies on zeolitic adsorbents, we developed a superior chromatographic material based on certain ion forms of chabazite. The chabazite-based chromatographic packing reported here is a versatile adsorbent and has the unique ability to quantitatively separate argon from oxygen a t ambient temperatures. We also found that treating the chabazite in an oxidizing atmosphere a t elevated temperatures improved the resolution of oxygen and argon. This lowers the oxygen detection limit to that of the detector. In addition to practical methods for determining low-part-per-billion by volume (ppbv) levels of oxygen, we found the calcium chabazite useful for determining similar levels of Ne, Ar, N2, CHI, and CO. There are scattered reports of the utility of chabazite for gas separations. Other researchers disclose that calcium chabazite gives the highest nitrogen/oxygen selectivities of any known zeolite but do not mention or discuss its use in separation of argon from oxygen ( 2 ) . The data and experimental procedures they present suggest that the calcium chabazite was not thoroughly dehydrated and therefore would not separate argon from oxygen. Vaughan, using gas chromatography to study the influence of the cation on the adsorption properties of chabazite, showed a useful separation t 1989 American Chemical Society
