1958
Anal. Chem. 1988, 60, 1958-1964
amount of time transpired between analyses at the two sites. The samples were quite varied in their viscosity and color (protein concentration). Some samples had a tendency to stratify in the test tube. This, combined with the small volumes available at the start, led to sample homogenizing difficulties.
LITERATURE CITED
CONCLUSIONS The multidimensional chromatographic approach demonstrates a practical use of micellar chromatography expanded beyond the singular dimensional chromatographic process. Methods development for this type of procedure is straightforward. The micellar mobile phase generally requires only modest modification for differing applications. The combination of micellar solvent and extraction phase is selected to provide the proper retention characteristics, the only restriction being that the solute must separate from excluded material. As in any HPLC procedure the extent of further optimization is dependent on the concentration level of drug to be determined. With improved reagent purification and modification in the multidimensional cycle it is realistic to expect LOD's in the low nanogram-per-milliliter level. Sample throughput can be increased by reducing the time necessary for washing and reequilibrating the extraction column and making use of faster analytical chromatography. Reduced diameter extraction columns are expected to provide this feature. It is expected and borne out by preliminary studies that only modest modifications will be required for multicomponent determinations.
(1) Wong, Steven H. Y. Therapeutlc Drug Monitoring and Toxicology by Liquid Chromatography; Marcel Dekker: New York. 1985. (2) Bdlingmeyer, B. A. LC Mag. 1984, 2(8), 578-580. (3) Zeif, M.; Crane, L.; Horvath, J. Am. Lab. (FaMleM, Conn.) 1982, 74(5), 120-130. (4) Pinkerton, T. C.; Miller, T. D.; Cook, S. E.; Perry, J. A.; Rateike, J. D.; Szczerba, T. J. Biochromatopaphy 1988, 7(2), 96-105. (5) Hagestam, 1. H.; Pinkerton, T. C. Anal. Chem. 1985, 57. 1757-1763. (6) Bargar, Ester M. J. Chrometop. 1987, 477, 143-150. (7) Smith, K. A.; Wood, S.; Crous, M. A. Anawst (London) 1987, 772 (April), 407-409. (8) Padrini, R.; Donatella, P.; Moretto, R. J. Chromtogr. 1987, 475, 183-187. (9) Weinberger, R. Ph.D. Dissertation, Seton Hall University, May 1984, 155-1 59. (10) DeLuccia, F. J.; Arunyanart, M.; Yarmchuk, P.; Weinberger, R.; Cline Love, L. J. LCMag. 1985. 3, 794. (11) DeLuccia, F. J.; Arunyanart, M.; Cline Love, L. J. Anal. Chem. 1985, 57, 1564-1568. (12) Arunyanart, M.; Cline Love, L. J. J. Chrometogr. 1985, 342, 293. (13) Armstrong, D. W.; Henry, S. J. J . L i q . Chromatogr. 1980, 3, 657-662. (14) Yarmchuck, P.; Weinberger, R.; Hirsch, R. F.; Cllne Love, L. J. Anal. Chem. 1982, 54, 2233-2238. (15) Granneman, G. R.; Sennello, L. T. J. Chromatogr. 1982, 229, 149. .. 157 . .. (16) Haginaka, J.; Wakai, J.; Yasuda, H.; Nakagava. T. Anal. Chem. 1987, 59. 2732-2734. (17) DorGy, J. G.; DeEchegaray, M. T.; Landy. S. J. Anal. Chem. 1983, 55,924-928. (18) Yarmchuck, P.; Weinberger, R.; Hirsch, R. F.; Cline Love, L. J. J . Chromatogr. 1984, 283, 47-60. (19) Armstrong, D. W.; Ward, T. J.; Berthod, Alaln Anal. Chem. 1988, 58, 579-582. (20) Lam, S., Albert Einstein College of Medicine, unpublished work, Jan 1987. (21) Wong, S., University of Connecticut School of Medicine, unpublished work, Jan 1987.
ACKNOWLEDGMENT The authors thank Stanley Lam of Albert Einstein College of Medicine for contributing the propranolol samples and S. H. Y. Wong from the University of Connecticut School of Medicine for contributing the chloramphenicol samples.
RECEIVEDfor review January 20,1988. Accepted May 2,1988. This work was presented in part at the 38th Pittsburgh Conference and Exhibition, Atlantic Citv. NJ, March 1987, Paper No. 198.
Adsorption Isotherm of Tetrabutylammonium Ion and Its Relation to the Mechanism of Ion Pair Chromatography J a n StPhlberg*J Astra Pharmaceutical Production A B , Quality Control, S-151 85 Sodertalje, Sweden Ingela Hagglund Department of Analytical Chemistry, University of Stockholm, S-106 91 Stockholm, Sweden
To understand the mechanlsm of Ion palr chromatography, a correct descrlptlon of the adsorption Isotherm of the amphlphlllc modifier Is Important. The adsorptlon Isotherm of tetrabutylammonlum Ion onto a RP-18 statlonary phase Is determlned wlth dffferent electrolytic counterlons (H2P04-,CI-, Br-) and for two dlfferent lonlc strengths. The electrostatlc surface potentlal created by the adsorbed tetrabutylammonlum Ions Is determined by applying the concepts of the electrostatic theory for Ion pair chromatography. The different experhnentally determined adsorption isotherms are found to colnclde wlth the same surface-potentlal-modlfled Langmulr isotherm. The results are therefore In accordance wlth the electrostatlc theory for Ion palr chromatography. Also affiliated w i t h the I n s t i t u t e o f Physical Chemistry, U n i v ersity o f Uppsala, Uppsala, Sweden. 0003-2700/88/0360-1958$01.50/0
The theoretical description of ion pair chromatography has been a subject of controversy for a number of years. A summary and analysis of the most important theories that appeared before 1985 is found in ref 1. These theories are mainly stoichiometric; i.e. the relation between the capacity factor and the concentration of amphiphilic modifier in the mobile phase is based on stoichiometric relations. Simple physical arguments show that any theory for ion pair chromatography must include the electrostatic surface potential created by amphiphiles adsorbed on the surface (2-4). The stoichiometric models are therefore p h y s i d y unrealistic. A hypothesis that proposes that the relative changes in the capacity factor for a charged analyte are due to changes in the electrostatic surface potential has been developed (2). This hypothesis has a number of consequences that can be used to test its correctness. An important consequence is that the capacity factor for an anal@ is described by a relation common to all analytes 0 1988 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 60, NO. 18, SEPTEMBER 15, 1988
1959
of different charges. This hypothesis has been shown to be bascially correct for a number of different analytes as well as amphiphiles (3). The isotherm of the amphiphilic modifier is fundamental to all theories for ion pair chromatography. It is usually treated as a Langmuir isotherm (1,5) or more empirically as a Freundlich isotherm (6,7).Bartha and Vigh measured the adsorption isotherm of several tetraalkylammonium ions and concluded that they cannot be described with either the Langmuir or Freundlich isotherms (8). To overcome the problem with the non-Langmuir behavior of the isotherm, the surface has been treated as heterogeneous with sites of different binding ability (9-11). For the adsorption of amphiphilies the stoichiometric adsorption equations are necessarily invalid because they do not consider the electrical double layer (12). The effect of the double layer on the isotherm has previously been considered by Cantwell (13) and Deelder and van den Berg (14) by calculating the surface potential from Stern-Gouy-Chapman theory. In this paper the surface potential is measured from changes in the capacity factor for ionic analytes. When the surface potential is known, its value is inserted in the equation for a modified Langmuir isotherm. The effect of ionic strength and type of counterion on the isotherm of tetrabutylammonium ion is studied. The stationary phase is RP-18, and the mobile phase is aqueous buffer/acetonitrile (90/10) at pH 2.1. The results are in excellent agreement with the electrostatic theory for ion pair chromatography and therefore give strong support to this theory.
and it is therefore possible to estimate the surface potential from changes in capacity factors. It is interesting to compare the measured surface potentials with theoretically calculated potentials obtained by solving the Poisson-Boltzmann equation. Such a comparison is difficult because of the complicated geometrical structure of the stationary phase. One difficulty is how to relate the amount of amphiphile adsorbed per gram of stationary phase to the concentration in moles per square meter. This is formally done by using the surface area as a conversion factor. The surface area is usually measured with the BET method using nitrogen as a probe molecule. For irregular materials, the surface accessibility for small molecules (e.g. N,) is larger than the surface accessibility for a large molecule. This is due to the inability of the larger adsorbate to follow the fine geometric irregularity of the surface of the stationary phase (15). The irregularity of the surface can be expressed by its fractal dimension (16),and it has been determined to be 2.97 for porous silica particles (In, which implies a highly irregular surface. In conclusion, the surface area determined from the BET isotherm cannot be used to calcualte the concentration of amphiphile on the stationary phase. In this paper the surface area is therefore an unknown constant that is determined from measured potentials with tetrabutylammonium ion as amphiphile. These are fitted to the theoretical curve obtained by solving the Poisson-Boltzmann equation in cylindrical coordinates. The solution of the linearized Poisson-Boltzmann equation in cylindrical coordinates is (18)
THEORY
Here nAis the concentration of surface charge in moles per square meter, K is the reciprocal Debye length, D is the dielectricity constant of the mobile phase, and eo is the permittivity of vacuum. &(Kr) and Il(Kr) are the modified Bessel function of the first kind of order zero and one, respectively. This equation can only be used for q0 < 40 mV. For higher surface potentials a numerical solution is used. Adsorption Isotherm for the Amphiphilic Modifier. The simplest possible adsorption isotherm, which considers the surface potential as well as a maximum possible concentration of amphiphile on the stationary phase, is derived in the following way. Consider the equilibrium
The basis for the electrostatic theory for ion pair chromatography is given in ref 2, so only a summary will be given here. The basic hypothesis of the electrostatic theory is that the equilibrium distribution of an analyte ion, B, is primarily determined by a chemical free-energy term, A G O B , and an electrostatic energy term, z$$@ The electrostatic energy term corresponds to the electrostatic work that is done on B when it is transported from the bulk of the mobile phase to a charged surface. In ion pair chromatography the surface of the stationary phase is charged because the amphiphilic modifier has a higher affinity to it than the counterions in the electrolyte have. The following equation for the capacity factor is obtained:
where 4 is the phase ratio. The surface potential is primarily dependent on the concentration of amphiphilic modifier on the surface, i.e. through the isotherm on its concentration in the mobile phase. Assuming that AGOB is independent of the surface potential, eq 1 can be written as
*' =
A(1)
nAFIo(Kr) K@I1(KT)
+ S = AS
$o =
RT kb,B In 7 ZBF
c,B
(3)
(5)
where A(l) and AS represent the amphiphile in the mobile phase and on the stationary phase, respectively. S is the part of the surface that is not occupied by the amphiphile. The condition of equilibrium is such that PAS
= PA + PS
(6)
where p represents the electrochemical potential for each species. The electrochemical potential for a positively charged amphiphile is in the ideal case as follows:
+ RT In CA Ps = b o s + RT In X S = poA
where kb,B is the capacity factor for B at some reference composition of the mobile phase for which the difference in electrostatic potential between the mobile and stationary phases is set to zero. In ref 3 some qualitative aspects of this equation were tested with a number of amphiphiles and analytes. It was found that the basic assumption holds well in most cases. Equation 2 can be written
(4)
(7)
where
xs + X A S
=1
(10)
Here cA,XS, and XAS are the concentration of amphiphile in the mobile phase and the fractions of unoccupied and occupied surface, respectively; po represents the electrochemica! potential for the standard state; $o is the surface potential, and F is the Faraday constant. By combination of eq 6-9 the following equation is obtained at equilibrium:
$960
ANALYTICAL CHEMISTRY, VOL. 60, NO. 18, SEPTEMBER 15, 1988
The fraction of the stationary phase surface that is occupied by amphiphilic molecules is XAS = nA/IZ0 (12) where no is the monolayer capacity of the surface and nA is the surface concentration of the amphiphile. The expression for the adsorption isotherm is obtained by combining eq 10-12.
Equation for Surface Potential When the Counterions in the Electrolyte Adsorb on the Stationary-Phase Surface. The surface potential as a function of surface charge density is obtained by solving the Poisson-Boltzmann equation. When the amphiphile is the only ion that adsorbs on the surface, the surface charge density equals the surface concentration of amphiphile. If, however, a counterion is adsorbed on the surface, the surface charge density is lower than the surface concentration of amphiphile. According to the electrostatic theory, the electrochemical potential of adsorbed counterions is p x = yoxs
+ RT In Xxs + zxFG0
(24)
The condition of equilibrium is This is a Langmuir type of isotherm where the effect of the surface potential is considered. It is important to note that this is the adsorption isotherm for the charged amphiphilic modifier. It depends on the concentration and type of counterion in the electrolyte only through the surface potential. Adsorption Isotherm of the Amphiphile Including Specific Interactions with the Counterion in the Electrolyte. The adsorption isotherm in eq 13 does not include the possibility of specific interaction between the amphiphilic modifier and its counterions. Assume that this interaction is described by the process A(1) X(1) S e AXS (14)
+
+
where X(l) is a counterion to the amphiphile A and AXS represents the complex formed due to specific interactions. In some models for ion pair chromatography the adsorption of A is solely described by the equilibrium in eq 14 (cf. ref 5). We will now derive the equation for the adsorption isotherm when the processes in eq 14 and 5 are simultaneously considered. The electrochemical potentials for AXS and X(1) are PAXS
= PoAXS + RT In XAXS RT In cx
px = p o x
+
(15) (16)
where XAXs is the fraction of sites occupied by AXS. The conditions of equilibrium are
+ I S = PAS + PX + PS = PAXS PA
PA
(17)
(18)
where llA,~ sand , PAS are the same as in eq 7-9. The relation between the fractions of occupied and unoccupied sites is XS + XAS + XAXS = 1 XAXS = n A X / n O (19) where nAXis the surface concentration of AX. Combining eq 15-18 and 7 gives
Combining eq 20 with eq 19 and 12 gives the following of after rearrangement:
By adding eq 21 and 22 and rearranging, we obtain the following equation for the adsorption isotherm:
(25) Px + PS = Pxs Combining eq 16 with eq 24 and 25 and assuming that the adsorption isotherm is linear in the investigated interval gives
nx = n6(XcXe-zXF+o/RT
(26)
It is possible to test this hypothesis by making an analysis of the potential as a function of the concentration of amphiphile on the stationary phase. Assuming that there are no specific interactions between the adsorbed amphiphile and its adsorbed counterion, the surface charge density, n, is n = nA - nx (27) where nx is the surface concentration of the counterion. From the solution of the Poisson-Boltzmann equation a theoretical function q0 = f(n) is obtained, i.e.
nA - Kxcxno exp
(-F “FGo))
(28)
where nA and n are the experimentally found and the theoretically calculated surface concentrations, respectively, for a given surface potential. EXPERIMENTAL SECTION Apparatus. A Waters Associates chromatography pump, Model 510, was used, and the detector was a Pye Unicam 4020 UV detector measuring at 255 nm. The injector was a Rheodyne Model 7125 with a 5-pL loop. The column was a CI8 LiChrosorb (25 cm X 4.0 mm i.d.; Hibar; Merck.) A water bath, HETO Type 01 T 640 (Birkerod, Denmark),was used to thermostat the solvent reservoir. The pH measurements were performed with a Radiometer PHM 82 standard pH meter equipped with a Radiometer combined electrode. The photometric determinations were performed with a Hewlett-Packard UV/Vis spectrophotometer, Model 8450. Chemicals and Reagents. As analyte ions (B) the following substances were used: lidocaine (2-(diethylamino)-N-(2,6-dimethylpheny1)acetamide) of pharmacopoeial grade supplied by Astra Pharmaceutical Production AB, Sodertiilje,Sweden; benzyltrimethylammonium chloride, benzyltriethylammonium chloride (Merck, Schuchardt);benzenesulfonic acid sodium salt, naphthalene-2-sulfonic acid sodium salt, and phenol from Merck, Darmstadt. The amphiphilic modifier (A) was obtained from Fluka (tetrabutylammonium chloride). Picric acid from Merck, (Darmstadt, was used when isotherm measurements were made. NaBr from Mallinckrodt, NaCl from Fluka AG, and NaH2P04and H3P04 from Merck, Darmstadt, were all of analytical grade and were used as electrolytes in the mobile phase. All solvents were of analytical or HPLC grade and were used without further purification. ChromatographicTechnique. The mobile phase consisted of phosphate buffer and acetonitrile in the volume ratio 91. The pH of the phosphate buffer was 2.0-2.2, and the electrolyte composition of the mobile phase was 0.097 and 0.190 M H2P04in the experiments with phosphate buffer. only. When the electrolyte was mixtures of counterions, the composition was (0.0048 M H2P04-and 0.086 M Br-) and (0.0048 M H2P04-and 0.086 C1-). The analyte ions were injected after dissolution in
ANALYTICAL CHEMISTRY, VOL. 60, NO. 18, SEPTEMBER 15, 1988
1961
Table I. Surface Potential ($,, mV) Measured with Different Analytes for Different Mobile-Phase Concentrations (cA, M) and Surface Concentrations (nA,mol in the Column) of Tetrabutylammonium Ion 103cA,4
M
0 0.05 0.08 0.10 0.25 0.50
1.00 2.00 4.00
10.00
106nA,
mol
benzenesulfonate
lidocaine
$o,*
mV
0
0
0
0
0
0
12.1 17.1 19.0 33.3 41.2 51.9 63.7 67.2 75.4
13.5 18.7 20.9 36.7
16.4 20.7 22.4 35.5 43.2
18.1 23.0 24.7 38.3 46.6 57.5 68.3
9.5 13.5 14.9 26.1 32.7 41.0 48.0 58.2 69.0
10.8 15.3 16.7 29.7 37.0 46.5 55.9 62.7 72.2
0 1.04 1.58 1.73 3.51 5.09 6.22 8.57 11.0 12.7
surface potential, IL0 (mV), for naphthalenebenzyltrimethylbenzyltriethyl2-sulfonate ammonium ammonium
'Mobile phase: acetonitrile/water (10/90) containing 0.097 M HZPO;; pH tentials.
2.1. b$o
is the mean of benzenesulfonate and lidocaine po-
Table 11. Surface Potential ($o, mV) Measured with Different Analytes for Different Mobile-Phase Concentrations (cA, M) and Surface Concentrations (nA,mol in the Column) of Tetrabutylammonium Ion 103~~:
M 0
0.05 0.10 0.25 0.50 1.00 2.00 4.00
10.0 30.0 100.0
106nA,
mol 0
1.12 2.04 3.63 5.43 6.87 9.07 11.4 14.8 21.2 28.1
benzenesulfonate -0 8.23 14.9 24.8 35.1 41.3 50.4 58.6 66.7 74.9
naphthalene2-sulfonate
surface potential, ibLn(mV), for benzyltrimethylbenzyltriethylammonium ammonium
-0
where tois the retention time of an unretained component, i.e. water. AU chromatographic results reported are the means of duplicate injections. Determinations of the amount of tetrabutylammonium ions adsorbed on the stationary phase were made by stripping the column with 1250 mL of acetonitrile/water (80/20). After evaporation the sample was diluted with phosphate buffer, and the tetrabutylammonium ion was determined photometrically by the picrate extraction method according to Gustavii (19). The total amount of tetrabutylammonium ion found was corrected for by using 0.7toas the total volume of solvent within the column (the flow through the column was 0.7 mL/min).
RESULTS The adsorption isotherm of tetrabutylammonium ion onto a chemically modified silica, RP-18 (LiChrosorb), was determined with a mobile phase containing different electrolyte counterions and ionic strengths. The composition of the solvent in all experiments is acetonitrile/water (10/90) with pH 2.1 f 0.1. In Figure 1 are shown the experimentally determined adsorption isotherms of tetrabutylammonium ion for the different compositions of the electrolyte. It is evident that the amount of tetrabutylammonium ion adsorbed a t a given mobile phase concentration increases as the ionic
14.8 20.9 31.7 40.1 49.4 61.1 73.8
13.0 17.9 28.2 36.0 44.2
'Mobile phase: acetonitrile/water (10/90) containing 0.190 M HzPO,-; pH tentials. the mobile phase. After passage of 50 mL of the mobile phase, the system was arranged for recirculation with 250-500 mL of mobile phase in the reservoir. The flow rate was 0.70 mL/min throughout all ofthe studies, and the mobile phase reservoir was thermostated in a water bath at 300 K. Retention time tR was converted to capacity factor k' via the relationship k' = ( t R - t o ) / t o
-0
-0
9.34 16.4 27.1 39.0 45.9
.
2.1. b$o is
lidocaine -0 7.61 12.4 20.7 27.5 34.6 41.2 52.7 62.9 69.9
ihb
mV 0
7.92 13.7 22.7 31.3 37.9 45.8 55.6 64.8 72.4
the mean of benzenesulfonate and lidocaine po-
strength is increased and when the HzP04-ion is exchanged by C1- and Br-. The electrolyte composition of the mobile phase is not strictly constant in an experimental series because tetrabutvlammonium chloride is added to the mobile Since the added tetrabutylammonium chloride constitu&s less than 10% of the total electrolyte, its effect on the isotherm can be neglected. The capacity factor for a number of positively and negatively charged analytes was also determined with this mobile phase containing different counterions as a function of tetrabutylammonium ion concentration. It has previously been shown that the electrostatic theory holds well when tetrabutylammonium ion is used as the amphiphilic modifier with another RP-18 stationary phase (Bondapak) (3). From eq 3 it is possible to calculate the surface potential experienced by different analytes, and the results are presented in Tables
1-111. The surface potential is set to zero for the amphiphile free system containing 0.097 M HzP04- (see Table I). No significant change of the capacity factor between this system and amphiphile free systems containing 0.190 M HzPO; or 0.0048 M H2P04-and 0.086 M NaCl was found (see Tables I1 and 111). This indicates that there is no preferential adsorption of sodium, phosphate, or chloride ions on the surface. However, when the system contained bromide ions (Table 111),a negative value for the surface potential is obtained. The explanation is probably that there is a preferential adsorption of bromide over sodium ion on the surface. From the tables it is apparent that different analytes experience somewhat different surface potentials. There are many physical processes that may be the origin of these
1982
ANALYTICAL CHEMISTRY, VOL. 60, NO. 18, SEPTEMBER 15, 1988
Table 111. Surface Potential (&, mV) Measured with Different Analytes for Different Mobile-Phase Concentrations (cA,M) and Surface Concentrations (nA,mol in the Column) of Tetrabutylammonium Ion surface potential, $ J ~(mV), for counterion bromide
chloride
103c~,' M
106n~, mol
0 0.05 0.10 0.25 0.50 1.00 2.00 4.00 10.00 0 0.50 2.00 10.00
benzenesulfonate
naphthalene2-sulfonate
benzyltrimethylammonium
benzyltriethylammonium
-5.63 4.38 9.53 20.3 28.1 35.1 41.7 47.4 53.4 -0 35.3 51.6 66.0
-4.45 6.41 11.4 23.2 31.0 38.5 45.5
-5.58 8.99 14.5 22.9 31.0 41.1 50.3
-4.02 11.9 18.3 27.2 36.4 46.6 56.9 68.7 82.8 -0 40.2 60.7
0 1.24 2.07 4.07 6.00 7.98 11.1 14.6 18.6 0 5.09 9.06 15.5
-0 37.0
-0 36.8
$Osb
lidocaine
mV
-5.17 2.60 7.70 14.5 21.6 28.7 35.7 42.8 51.5 -0 28.8 43.8 62.6
-5.40 3.49 8.62 17.4 24.9 31.9 38.7 45.1 52.4 0 32.0 47.7 64.3
"Mobile phase: acetonitrile/water (10/90): containing 0.086 M NaBr or NaCl and 0.0048 M HZPOL; pH 2.1. *$o is the mean of benzenesulfonate and lidocaine Dotentials. n,
n,. 11 ;mol)
I O 5 (mol)
*,I
20
15
10
5
t
0; 0
2
,
4
I
6
I
8
10 c,(mM)
Figure 1. Adsorption isotherms of tetrabutylammonium ion onto RP-18 from a mobile phase containing CH,CN/H,O (10/90) at pH 2.1 and 0.190 M different electrolyte compositions: (X) 0.097 M H2P04-, (0) 0.086 M CI- and H2P0,-, (A)0.086 M Br- and 0.0048M H2P04-, (0) 0.0048M H2P04-.
differences. For some of these processes, e.g. amphiphileanalyte correlation and competition for sites, the difference between negatively and positively charged analytes tends to cancel. Other processes are related to specific physical properties of the analyte-amphiphile-stationary phase, e.g. monopole-dipole interaction in the surface layer. The most important point for this study is that the potential is measured with the same analytes in all experiments and that the charges of the analytes are of opposite sign. The surface potential used in the calculations below is taken as the mean value of its value for benzenesulfonate and lidocaine. Most of the conclusions in this paper are unchanged even if the measured potential deviates from the true potential by a constant value. The possibility of a varying deviation between measured and true surface potentials in an experimental series cannot be excluded, but it will probably be less than 5 mV in all cases. When the surface potential is known, it is possible to test the isotherms given by eq 13 and 23. In Figure 2 the amount of tetrabutylammonium ion adsorbed, nA, is plotted as a function of CA exp(-F$o/RT) for the four different electrolyte systems. In this plot the four originally distinct adsorption isotherms given in Figure 1 are rationalized into a single
ANALYTICAL CHEMISTRY, VOL. 60, NO. 18, SEPTEMBER 15, 1988 c,'e
1963
-WdRT
n, 105 (mol)
+
XX
0
0
I
0.50
,
1-00
i.'w
* -Wdm M . W
c,e
Figure 3. Test of the surfacapotentlal-correctedLangmuir adsorption isotherm according to eq 29. Symbols are the same as in Figure 2.
scattering of the data at lower concentrations is probably due to small experimental errors. That these errors are unimportant is seen in Figure 2, where the full line represents the adsorption isotherm, eq 13, calculated from the obtained values for no and KAS. In a separate measurement using 100 mM tetrabutylammonium chloride added to the system containing 0.190 M H,PO,, the amount of adsorbed tetrabutylammonium ion was found to 2.81 X lo4 mol. The good agreement between the two separately determined values and the good adherence to a straight line show that the isotherm follows eq 13. The adsorption isotherm that considers nonspecific electrostatic interactions as well as specific interactions is given by eq 23. The influence of the specific interaction term on the isotherm will be illustrated by using the experimental isotherm with bromide as counterion as an example. Equation 23 can be rewritten as
I
0
c,e -WdN ~ . 1 0 3
1.10
I
0.80
0.40
Flgure 4. Test of the adsorption isotherm that considers both the surface potential and specific interactions between tetrabutylammonium ions and bromide ions (eq 23).
/ x
40-
20-
0
f
I
I
2
4
6
-
1
When the concentration of tetrabutylammonium ion in the mobile phase is 10.50mM, the denominator can be neglected. From the slope of the surface-potential-modified adsorption isotherm and from the found value for no (2.77 X 10"' mol), the following relation is obtained:
Flgure 5. Comparison between the solution of the Poisson-Boltzmann equation and the experimentally obtained surface potentla1 as a function of surface charge density. Mobile phase: CH3CN/Hz0 (10/90), pH 2.1, containing 0.097 M HzPO,- (X) and 0.190 M (0). Surface area of the column was 166 m2.
The isotherm is then calculated for different ratios of K A x s c X / K ~There is a difference between the numerical values of n&* obtained from the slope of the linear part of the isotherm and from the intercept of the Langmuir plot. When the lowest of these values is used in eq 31, the resulting adsorption isotherm will favor the ififluence of specific interactions. The result is presented in Figure 4,where it is seen that the maximum possible contribution of specific interactions to the adsorption isotherm is about 10%; i.e. when KAX~CX/KAS = 0.1, it fits the experimental isotherm. By solving the Poisson-Boltzmann equation, one obtains the relation between surface potential and surface charge
density, i.e. the concentration of tetrabutylammonium ion on the surface. In this paper a numerical solution of the Poisson-Boltzmann equation for a cylindrical geometry is used where the diameter of the cylinder is set to 75 A. The Debye length in the investigated systems is 10 8, or less, and the surface potential as a function of surface charge density is therefore nearly independent of the chosen radius as long as it is >40 A. Since the used silica is considered to have a pore radius of 100 A, it is reasonable to assume that the actual pore size distribution would have a minor influence on the agreement between the calculated and experimentally obtained relation between surface potential and surface charge density. In Figure 5 is shown the experimentally obtained surface potentials as a function of the amount of adsorbed tetrabutylammonium ion on the surface for the two investigated
Hm,-
1964
ANALYTICAL CHEMISTRY, VOL. 60, NO. 18, SEPTEMBER 15, 1988
1
/
i;;';
a L1
a
/
40 -
i To
x
i
A D
\
/
20 -
7"
0-
7" a
,
0
Flgure 6.
1
2
1
I
4
6
8
10
-
n,moVm2. 10'
Test of eq 28. Plots show the measured surface potential
when bromide (A)and chloride (0)are counterions and the surface
potential after correction for adsorption of bromide (X) and chloride (0). Full line represents the solution of the Poisson-Boltzmann
equation.
phosphate buffer systems. The corresponding theoretical functions are obtained from fitting its slope to the linear part of the experimental function. As has already been discussed, the surface area of the stationary phase is an unknown system constant in these calculations. There is a good agreement between the numerical value of this constant determined in these systems, 167 and 166 m2,respectively. It is also seen that the agreement between the theoretically and experimentally obtained functions is good. This indicates that the Poisson-Boltzmann theory is useful for describing the electrostatic properties of the investigated system. The theoretical relation between surface potential and surface concentration of amphiphile for the case when an electrolyte counterion is adsorbed on the surface has been given in the theory section. It was found that it is possible to determine the distribution constant of the counterion by plotting (nA- n) as a function of exp(-zxF$o/Rl") for a given surface potential; see eq 28 where nAis the experimentally found surface concentration of tetrabutylammonium ion at a given surface potential and n is the theoretical surface charge density a t that surface potential. The system where the bromide ion has been substituted for phosphate is used to test this theory. The experimentally obtained surface potential as a function of the amount of adsorbed tetrabutylammonium ion is shown in Figure 6 (A). The full line represents the theoretical function calculated from the Poisson-Boltzmann theory. In the figure is shown the experimentally found surface potential after correction for KBrcBrnO, indicated by (X). Also shown is the experimentally obtained surface potential when chloride is counterion (0) and the corrected potential (0) obtained by using the value 0.352 X for KclccIno. It is apparent that the agreement between experimental results and the proposed theory is good in both cases. CONCLUSIONS The purpose of the presented work is to investigate the consistency of the electrostatic theory for ion pair chromatography. I t is found that the agreement between the electrostatic theory and experimental results is very good. The conclusion is therefore that the interaction between adsorbed tetrabutylammonium ions and the counterions in the elec-
trolyte (H2P04-,C1-, Br-) is described by nonspecific electrostatic interactions. This conclusion is based on the fact that when the surface-potential-modified Langmuir isotherm is used, a common isotherm is found in all the investigated systems (see Figure 2). This means that the origin of the different adsorption isotherms of the tetrabutylammonium ion (see Figure 1) are due to differences in the surface potential. The surface-potential-modified Langmuir isotherm, eq 13, is shown to hold well (see Figure 3), and the calculated monolayer capacity agrees well with the value experimentally obtained. The term in eq 23 describing the formation of AXS is therefore negligible (see Figure 4). Differences in the surface potentials between the systems containing different amounts of phosphate buffer are described by the Poisson-Boltzmann equation (see Figure 5 ) . This means that. there is no specific adsorption of Na+ or H,PO, ions to the surface layer and that there are no specific interactions between adsorbed tetrabutylammonium ions and H2P04-ions. When Br--ions are used as counterions, they are adsorbed on the surface, which consequently alters the surface potential. Their influence on the surface potential is described by using a distribution constant to the surface and nonspecific electrostatic interactions (see Figure 6 and eq 28). That the obtained differences in surface potentials between the different electrolyte systems are described by nonspecific electrostatic interactions is consistent with the conclusion drawn from the isotherm experiments. The prevailing view, that the mechanism of ion pair chromatography is an exchange between a counterion and an analyte ion, is therefore shown to be incorrect in the investigated systems. ACKNOWLEDGMENT We are most grateful to M. Almgren and B. Jonsson for valuable discussions during the preparation of this work and to A. Furangen for valuable discussions of the manuscript. The computer program for a numerical solution of the Poisson-Boltzmann equation was obtained from the Division of Physical Chemistry I, Chemical Center, University of Lund, Lund, Sweden, and was kindly put at our disposal by B. Jonsson. The program is available from the corresponding author. Registry No. Tetrabutylammonium, 10649-76-5; silica, 7631-86-9. LITERATURE CITED (1) Melander, W. R.; Horvath, C. Chromatogr. Sci. 1985, 31,27. (2) StBhlberg, J. J. Chromatogr. 1986, 356, 231. (3) Stahlberg, J.; Furangen, A. Chromatographia 1987, 24, 783. (4) Stahlberg, J. Chromatographia 1987, 2 4 , 820. (5) Tilly Melin, A.; Askemark. Y.; Wahlund, K.-G.; Schill, G. Anal. Chem. 1979, 51,976. (6) Deelder, R. S.;Linssen, H. A. J.; Konijendijk, A. P.; van de Venne J. L. M. J. Chromatogr. 1979, 185, 241. (7) Knox, J. H.; Hartwick, R. A. J. Chromatogr. 1981, 2 0 4 , 3. (8) Bartha, A.; Vigh, G. J . Chromatogr. 1983, 260, 337. (9) Tilly Melin, A.; Ljungcrantz, M.; Schill. G. J. Chromatogr. 1979, 185, 225. I O ) Sokolowski, A,; Wahlund, K.-G. J. Chromatogr. 1980, 189, 229. 11) Jansson, S. 0.; Anderson, I.; Persson E. A. J. Chromatogr. 1981, 203,93. 12) Davies, J. T.; Rideal, E. K. Interfacial Phenomena, 2nd ed.;Academic: New York, 1963; Chapter 4. 13) Cantwell, F. F.; Puon, S.Anal. Chem. 1979, 51. 623. 14) Deelder, R. S.;van den Berg, J. H. M. J. Chromatogr. 1981, 218. 327. (15) Meyer, A. Y.; Farin. D.; Avnir. D. J. Am. Chem. SOC. 1986, 108, 7897. (16) Mandelbrot, B. 6.The Fractal Geometry of Nature; Freeman: San Francisco, 1982. (17) Farln, D.;Volgert, A,; Avnir, D.J. Am. Chem. SOC. 1985, 107, 3368. (18) Rice, R. E.; Horne, F. H. J. Colloid Interface Sci, 1985, 705, 172. (19) Gustavii, K.; Schill, G. Acta Pharm. Suec. 1986, 3 , 241.
RECEIVED for review February 2, 1988. Accepted April 20, 1988.
