Anal. Chem. 1991,63,2032-2037
2032
separations dramatically (22-24). While we have restricted attention to linear inlet gradients, similar effects could obviously arise for concave and convex gradients. Shocks could occur even sooner with convex gradients and later for concave gradients (which would tend to become more linear). The resulting effect on adsorbate separation would be along the lines of the foregoing discussion.
CONCLUSIONS The effect of accounting for the adsorption of the mobilephase modulator in gradient elution is examined quantitatively through numerical simulations for reversed-phase chromatography with water-acetonitrile as the mobile phase. The adsorption of the modulator gives rise to gradient deformation and, under extreme conditions, to the formation of a modulator shock layer. The possible consequences of such a shock layer on gradient separations include extreme concentration of adsorbates that lie just behind, or straddle, the shock layer and shoulders (“false peaks”) on either the leading or the trailing edge of the band. Experimental verification is being attempted in our laboratory. ACKNOWLEDGMENT We thank Richard Hendrickson, Paul Westgate, and Yiqi Yang for their helpful comments on the manuscript. LITERATURE CITED (1) Snyder, L. R.; Kirkland, J. J. Inlroducnron to MoaKn Chrometography, 2nd ed.;Wliey: New York, 1979; Chapter 16.
Snyder, L. R. I n High Performance Lipuld CkomatqaphyAdvances and Perspeclives;b a t h , Cs.. Ed.; Academic Press: New YO&, 1980 Voi. 1, pp 208-316. Snyder, L. R. I n High Performance LlquM ChromatcgraphyAdvances 8nd Pempsctives; m a t h , Cs., Ed.; Academic Press: New YO& 1986; Voi. 4, pp 195-312. Jandera. P.; Churacek, J. &adient Elution In LiquM Chromatography. Theory and P r a c t h ; Ekvler: Amsterdam, 1965; Chapter 4. Levin, S.; Grushka, E. Anal. Chem. 1986, 58, 1602-1607. Levin, S.; Grushka, E. Anal. Chem. 1987, 5 9 , 1157-1164. Oolshan-Shhazl, S.; Gukhon, 0. J . chrome-. 1989, 461, 1-16. Goishan-Shirazl, S.; Guiochon, G. J . Chromatogr. 1999, 461, 19-34. DeVault, D. J . Am. Chem. Soc.1943, 65, 532-540. (Wueckauf, E. Roc. R . Soc. London 1948, A186, 35-57. Rhee, H.-K.; Bodin, 8. F.; Amundson, N. R. Chem. Eng. Sci. 1971, 26, 1571-1560. Velayudhan, A.; Ladisch, M. R. Chem. Eng. Scl., in press. Yamamoto. S.; Nakamishi, K.; Matsuo, R. Ion €xd?angeChromatography of Proteins; Marcel Dekker: New York, 1968, pp 217-221, 265-277. Frey, D. D. Biotechnol. Bloeng. 1990, 35, 1055-1061. Keulemans, A. I. M. Gas Chromatography; Reinhold: New York, 1957; pp 106-129. Fritz. J. S.; Scott, D. M. J . Chromatogr. 1993, 271, 193-212. Karol, P. J. Anal. Chem. 1989, 61, 1937-1941. Lln, 8.; Ma, 2.; GuiWhon. G. J.BMW?IBtw. 1989, 481, 63-102. Slaats, E. H.; Markovski, W.; Fekete, J.; Poppe, H. J . Chrometogf. 1981, 207, 299-323. Tani, K.; Suzuki, Y. J . ChrMetOgr. Sci. 1989, 2 7 , 698-703. Tklius, A. Angew. Chem. 1955, 67. 245-251. Snyder, L. R. Mncipks of Adsorption Chromatography; Marcel Dekker: New York, 1968; pp 206-208. BoehtM, W.; Engelhardt, H. J. Chmmatogr. 1977, 133, 87-81. Paanakker, J. E.; Kraak, J. C.; Poppe, H. J . Chfomatogr. 1978, 149, 111-128.
RECEIVED for review March 5,1991. Accepted June 7,1991. This work was supported by NSF Grants CBT8351916 and BCS8912150.
Electrical Double-Layer Model for Ion-Pair Chromatographic Retention on Octadecylsilyl Bonded Phases Hanjiu Liu and Frederick F. Cantwell* Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
Sknuttaneow sorptkn of the p-nttrobenzenesutfonate sample k n (NBS-) and tetra-n-butylammonh “palrlng Ion” (TBA’) was measured by the column equlllbratlon technlque as a functlon of both TBA’ concentratlon and total lonk strength. The surface exceas of TBA’ vades wkh lonk strength. From H can be calculated both the anlon-exchange capaclty and the surface electrical potentlal, q0. The latter Is constant at a constant actlvlty of TBA’ In solution, am. Experlmental plots of the dlstrlbutlon coefflclent of NBS- versus Ionic strength, at constant anA, were fH quantttatlvely by a prevloudy derived equatlon h whkh two procesuos are acrtuned to be respondble for NBS- sorptkn. dynamlc a n h exchange In the dlffuse part of the electrlcal double layer and surface adsorptlon. Dependlng upon experlmental condHlons, It Is posslble for etther Ion exchange or surface adborptlon to become a domlnant process. Thls may explain why prevlous workers have Invoked etther dyrrsmlc lon exchange or surface adsorptlon, but not both, to explain “Ion palr” retentlon.
INTRODUCTION In the technique called ion-pair chromatography, which is usually performed on a reversed-phase packing, a large 0003-2700/91/03632032$02.50/0
hydrophobic ion is added to the mobile phase in relatively high concentration in order to increase the retention of small sample ions of opposite charge (I). It has long been known that in this kind of chromatography the large “pairing ionn is sorbed onto the packing. This knowledge led to the idea that the process responsible for retention of the sample ion should be viewed as ’dynamic ion exchange” rather than “ion-pair” sorption (2-8). In an early paper (9) it was shown that the sorption of an organic ion onto a reversed-phaseadsorbent could be explained quantitatively in terms of the Stern-Gouy-Chapman model of the electrical double layer and it was suggested that an electrical double-layer model would explain the sorption of the large pairing ion onto a reversed-phase bonded-phase packing such as octadecylsilyl silica (ODs). Subsequent studies have verified this (10-20). In order to obtain basic information about the processes that might be responsible for sorption of a sample ion in the presence of an excess of sorbed pairing ion, studies were performed on the sorption of small sample ions onto reversed-phase adsorbents that possessed low-capacity ion-exchange character as the result of sulfonate groups or quaternary ammonium groups covalently bound to the surface (21-23). These studies revealed that sample ion sorption could be expressed quantitatively in terms of two processes: (i) ion 0 1991 American Chemical Society
ANALYTICAL CHEMISTRY, VOL.
exchange of the sample ion with ions of like charge present in the diffuse part of the electrical double layer; (ii) adsorption onto the electrically charged surface. The latter process is strongly dependent on the magnitude of the electrical potential at the surface +o, which is given by SGC theory. Based on these observations, a model was suggested (21) and later was derived in detail (241,for ion-pair retention of a sample ion in the presence of a reversibly sorbed pairing ion. The model included both surface adsorption and dynamic ion exchange in the electrical double layer. The proposed model is quite consistent with the well-established principles of surface and colloid chemistry (25). In the context of bonded-phase packings the term “adsorption” can be taken to be either adsorption onto the bonded-phase/mobile-phaseinterface or partitioning into a pseudoliquid bonded phase, without prejudice to the double-layer model (10). Over the last few years other workers have employed various versions of the electrical doublelayer model to explain ion-pair retention. They have tended to invoke either dynamic ion exchange (11,26,27)or adsorption (12-191, but not both, to explain retention of the small sample ion on a bonded phase coated with the large pairing ion. A few workers who suggested that dynamic ion exchange was the main sorption process for the sample ion also found it necessary to invoke some sort of additional sorption process which they called “desolvation” (28,29)or, less specifically, a “second effect” (30). Although one group (30) recognized that this additional process depended on ionic strength of the mobile phase, neither group recognized the important role played by the surface potential, *OS
In a recent paper we showed that sorption, onto an ODS bonded phase, of the tetra-n-butylammonium cation (TBA+) from a solution of its chloride salt and, separately, of the p-nitrobenzenesulfonate anion (NBS-) from a solution of its sodium salt are both quantitatively described by the SGC model (IO). In the presently reported study we have TBA+ present in relatively high concentrations as the pairing ion and NBS- present at trace concentrations as the sample ion. Under these typical ion-pair chromatography conditions we demonstrate experimentally that the previously proposed double-layer sorption model (24) quantitatively describes the sorption of the NBS- sample ions as the sum of both dynamic ion exchange in the diffuse layer and potential-dependent adsorption on the bonded phase. Experimentally, we use a column equilibration technique to measure the amounts of TBA+ and NBS- simultaneously sorbed, as a function of ionic strength.
THEORY A detailed development of the model has already been presented (23,24,31),as has relevant background information (9, 20, 21). Only the final equations are presented below. However, two important points require clarification. First, the model assumes that the sample ion (e.g. NBS-) is present at “trace conditions”. This means that it is present in the mobile phase at concentrations much smaller than those of other components and that it is present (sorbed) in the stationary phase in amounts much smaller than that of the total number of sorption sites. For the dynamic ion exchange contribution to sample sorption, the concept of trace conditions is the same as for conventional ion exchangers (32). For the adsorption contribution to sample sorption, trace conditions means that the number of adsorbed sample ions is so much smaller than the number of adsorbed pairing ions that their presence produces no significiant alteration either in the surface concentzationof pairing ion or in the surface potential, Go, which arises from the adsorbed pairing ions. In practice, trace conditions lead to a pairing-ion isotherm that is unchanged by the presence of sample ion and to a sample-ion
63,NO.
18, SEPTEMBER 15, 1991
2033
isotherm that is linear with zero intercept. Thus, trace conditions are easily verified experimentally and they are identical with the conditions that are desired chromatographically in order to perform linear elution chromatography. The second point requiring clarification is the fact that the model presupposes that sorption isotherms for the pairing ion are already accurately known (24). These isotherms may have been obtained by experimentallymeasuring them or they may have been predicted by some theory. In the present study we employ isotherms for the pairing ion TBA+ which were experimentallymeasured on Partisil-10 O D s 3 (10). One could attempt to predict the shapes of sorption isotherms for a pairing ion like TBA+ on an ODS packing by using a theoretical equation, such as a Langmuir equation modified to take into account double-layer affects (33). However, there is enough variability among ODS packings from different suppliers, and probably even among different batches from the same supplier, that a considerable amount of information (e.g. residual silanol concentration) would be required about a particular batch of ODS packing before the theory could be used to predict isotherm shapes. (See Discussion, Effects of Silanols on TBA+ in ref 10.) It is easier in practice and also more accurate to experimentally measure the sorption isotherms for the pairing ion on the ODS packing of interest. Ion Exchange of NBS- in the Diffuse Layer. The adsorption of TBA+ creates a (dynamic) anion exchanger in which the counterion C1- in the diffuse part of the electrical double layer is available for exchange with the sample counterion NBS- in the bulk solution. The dimensionless ionexchange equilibrium constant is defined as KIEX = (~DL,NBSYDL,NNBS) (CCIYCI) / (CNBSYNSS) (~DL,CIYDL,CI) (1)
where rDand rDba are the surface excesses of ms-and Cl- in the diffuse layer in mol/cm2, YDand Y D L are ~ ionic activity coefficients in the diffuse layer, C m and C” are molar concentrations in the bulk solution, and y m and ya are ionic activity coefficients in the bulk solution. Since NBS- and Clare both univalent and since trace conditions of ion exchange prevail for NBSYcl= YNBS
(2)
YDL,CI = YDL,NBS
(3) (4)
c = CC]
(5)
where rmAis the surface excess of TBA+ in mol/cm2 and c is the ionic strength of the bulk solution. The ion-exchange distribution coefficient for NBS- is defined as KhBS,iex E IIDL,NBS/CNBS
(6)
It can be expressed in units of (mol/kg)/(mol/L) in the following form, after combining eqs 1-6: KNBs,iex
= KIEXASP~TBA/C
(7)
Here ASP is the specific surface area of the ODS packing in cm2/kg. Also the “dynamic ion-exchange capacity” in units of mequiv/g is given by Qwt
= ASPrTBA
(8)
It is important to note that for a dynamic ion exchanger is dependent both on the concentration of TBA+ in the bulk solution, C,, and on the ionic strength c. This is shown by the isotherms in Figure 1,which were measured at various constant values of c. As a result of the direct proportionality in eq 7, the value of Kmjsl, between Km,isxand measured a t constant c, will change with CmA in the same
rm
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ANALYTICAL CHEMISTRY, VOL. 63,NO. 18, SEPTEMBER 15, 1991
The surface adsorption distribution coefficient for NBSis defined as K”BS,ads = I I A D S , N B S / h S (11)
It can be expressed in units of (mol/kg)/(mol/L) in the following way, after combining eqs 9-11:
21-----J
L 01
0.0
0.5
1.0
1.5
2.0
where PADS,NBS
2.5
[TBA’] x lo2 (mol/L) Figure 1. Sorption isotherms for the “pairing ion” TBA’ on Partisil-10 OD53 from pH 5.0 aqueous solution. Numbers by the curves indicate ionic strengths.
way that rmA does in the appropriate isotherm in Figure 1. The characteristics of the TBA+ isotherms in Figure 1 are discussed in detail in ref 10, including the steep rise from the origin to rmA 2.3 X lo-” mol/cm2 and the Langmuirian shapes above this surface concentration. On the other hand, if the dependence of KmS,iexon c is considered, the situation is more complex because changing c also causes rmA to change. If c is increased at a constant value of C ~ the A value of rmA also increases (Figure l), but the rate of its increase is usually much slower than the rate of increase of c itself. Thus, in eq 7,an increase in c will cause the ratio rmA/C to decrease. Consequently, when c is increased at constant CmA the value of Kms,iexdecreases, but not in direct proportion to c-l. Surface Adsorption of NBS-. The layer of TBA+ ions adsorbed at the ODS/mobile-phase interface (or dissolved in the ODs pseudoliquid phase, depending on one’s view) defines the charge surface (9). The electrical potential at the charge surface, in volts, is Adsorbed NBS- sample ions are considered to lie in this same charge surface, rather than to lie in an inner Helmholtz plane (9). They experiencethe potential The volume that contains the adsorbed ions is taken as the product of the surface area of ODS times the thickness of the compact part of the double layer (9,10). It is important to note that, even in the absence of TBA+ pairing ions, the NBS- ion is adsorbed on the ODS packing (10). The presence of a positive surface potential, +, enhances that adsorption. The dimensionless equilibrium constant for adsorption of NBS- is defined as
+,.
+,.
KADS
= 103rADS,NBSYADS,NBS/CNBSdYNBS
= P0ADS,NBS + RT In YADs,NBs
(13)
The thermodynamic reference state for eq 13, in which ymsm = 1, is defined as the hypothetical ODS surface that is free of all ions (i.e. TBA+ and NBS-), that is, ‘infinite dilution” on the surface. The surface activity coefficient, y m , ~in, eq 9 and 13 is different from an ionic activity coefficient (24). It is not related to ionic strength or electrical potential. Rather, it accounts for the fact that the value of /LADS,NBS may change due to the change in chemical character of the ODS surface as a result of increasing coverage by TBA+. The best analogy in homogeneous solution chemistry is the ‘transfer activity coefficient” that is used in dealing with solutes dissolved in different solvents but using infinite dilution in water as the reference state (34). The relationship between K m d and c can be understood as follows. The surface potential is related to the activity of the potential-determining ion TBA+ in bulk solution (Le. = CmAymA) perhaps, though not necessarily, via the Nernst equation (9, 10). In turn, YTBA is related to c (e.g. by the DebyeHuckel law at low c). Thus, at fired c , at which Y ~ and y m are constants, increasing CmA will increase in eq 12 and thereby increase K m a & On the other hand, if Cm is held constant, then increasing c will caw ym and, therefore, am to decrease. A decrease in Q ~ decreases A +,. From eq 12, decreasing yms and causes KNm,abto decrease. Overall Distribution Coefficient. The overall distribution coefficient of NBS-, K m r , is the sum of the two distribution coefficients given above:
+,
+,
K N B S=~KNBS,ier + KNBS,~~S
(14)
Combining eq 14 with eqs 7 and 12 gives the following expression for the overall distribution coefficient:
(9)
and is equal to
where rADS,mS is the surface excess in mol/cm2 due to adsorbed NBS-, 7m.mis the activity coefficient of NBS- on the surface, y m is the bulk solution activity coefficient, Cm is the molar concentration in bulk solution, d is the thickness of the compact layer in units of cm, 2-is the charge of -1 on the NBS- ion, p 0 m , m is the standard chemical potential in units of J/mol for the transfer of NBS- from bulk solution to the surface when = 0 V, F = 96481 C/mol, R = 8.314 J/(mol.K), and T = 298 K. The numerator term in the parentheses in eq 10 is an electrochemicalpotential. Equation 10 will be recognized to have the form of the well-known relationship between free energy (i.e. electrochemicalpotential) and equilibrium constant. The method for calculating +o from the amount of sorbed TBA+ has already been presented (10).
+,
As discussed above, c and CmA are the two mobile-phase variables affecting the sorption of NBS-. When C m is held constant, both Kmja and K m d decrease with increasing c , and when c is held constant, both Km,ier and Kms+a. increase with increasing CTBk Experimentally testing the validity of this retention model requires simultaneous measurement of the amounts of sorbed NBS- and TBA+ as functions of both C m and c. In the present study these experiments have been performed. The value of Kmc predicted by eq 15 is compared with the experimentally measured value of KNmr.
EXPERIMENTAL SECTION Materials. Chemicals and solvents have all previously been described (IO). The OctadeCyLsiylpacking material was Partisil-10 ODs-3(Batch No. 100763, Whatman Inc., Clifton, NJ), which is repoljed by the manufacturer to be highly “end capped“.
A
ANALYTICAL CHEMISTRY, VOL. 63,NO. 18, SEPTEMBER 15, 1991
A 600 7w[ 5O0
0.050
0.070
/ / j c
t
-0.0
0.5
1.o
1.5
2.0
2.5
[TBA’] X lo2 (mol/L) Flgure 2. DistrlbuHon coefficients for NBS- (eq 18) at trace conditions in the presence of TBA+, at five different ionic strengths. C, = 1.49 X lo-’ moilL. Numbers by each curve indicate ionic strengths. Corresponding surface excesses of TBA+ are shown in Figure 1.
Sample and Eluent Solutions. In the experiments that provided the results shown in Figure 2, five series of sample solutions were prepared, with each series at a different constant ionic strength. The five series were at ionic strength 0.050,0.070, 0.100, 0.300, and 0.500. Ionic strength was adjusted by adding NaCl. Within a series at a particular ionic strength, each solution contained a different concentration of the pairing ion, TBA+, in the range 0.0017 -0.0200 M. All solutions were adjusted to pH 5.0 with 1 x 10-9 M acetic acid/sodium acetate buffer and all solutions contained 1.49 X 10” M NBS- sample ion. In the experiment used to establish trace conditions for NBS-, two sets of sample solutionswere used, at ionic strengths of 0.500 and 0.050, respectively. All solutions contained 1.94 X M TBA+ and various concentrations of NBS- in the range 0.5 X lP to 2.5 X lo4 M, and all solutions were at pH 5.0. The eluent used to elute NBS-and TBA+from the column after achievement of column equilibration was methanol/water (1:1 v/v) containing 0.010 M NaCl. All solutions were filtered before use through a 0.45 pm pore size Nylon-66 filter (Rainin Instrument CO.).
Apparatus and Procedure. The column equilibration technique has previously been discussed (22, 35). The (pre)column, which contained 1.58 X g of the Partisil-10 ODs-3 packing to be studied was a commercial cartridge column (Part No. 28690, Chrompak, Netherlands) that was 0.20 cm long X 0.46 cm i.d. It was thermoatated in a water bath at 25.0 f 0.5 OC. The injection valve that held the (prelcolumn and the pumps used to deliver sample solution and strong eluent were as previously described (IO). The analytical column was a commercialcolumn of PRP-1 (Part No. 19425, Hamilton Co., Reno, NV). The injection loop used to deliver the calibrating standard solution of NBS- (valve V2 in refs 22 and 35) was a Model U6K (Waters h o c . ) . The HPLC detector at the outlet end of the analytical column was a Model 481, Lamda-Max spectrophotometer (Waters Assoc.) usually set at 266 nm to have maximum sensitivity for NBS-. A Model HP 3390A digital integrator (Hewlett-Packard)was used to obtain areas of eluted NBS- peaks. In the column equilibration experiment the sample solution containing =A+, NBS-, sodium chloride to adjust ionic strength, and pH 5.0 buffer was pumped through the column until equilibrium was achieved between the ODS packing and the solution. This was the loading step. Then the valve was switched to allow the strong eluent to elute TBA+and NBS-from the ODS column, through the analytical column to the detector. The effluent was collected to the mark in a 25-mL volumetric flask at the outlet of the detector. This was the elution step. The amount of NBS- on the ODs column was calculated from the area of its peak obtained with the UV detector. Since TBA+
2035
does not absorb UV light, the analytical column was not needed to separate NBS- from TBA+. Rather, the analyticalcolumn was used to separate NBS- from the water, which was washed out of the ODS column system by the eluent and which produced a “refractive index”peak in the W detector. The amount of TBA+ on the ODS column was calculated from its concentration in the 25 mL of effluent,which was measured by solvent extraction with picrate reagent using the technique of solvent extraction-flow injection analysis, as previously described (IO). Achievement of equilibrium between the ODS packing and the sample solution was experimentally tested for sample solutions containing various combinations of C m ,,C , and c by varying the sample loading time. For TBA+the necessary loading volume was never more than about 20 mL and for NBS- it was never more than about 100 mL. Therefore, 125 mL was always used in the loading step. Complete elution of both NBS- and TBA+ in a volume of eluent much less than 25 mL has previously been demonstrated (IO). The concentrations of both NBS- and TBA+ sorbed onto the ODS packing were calculated after subtracting the amounts in the hold-up volume of the (pre)column system (IO). The experimental distribution coefficient of the NBSsample ion was calculated as KNBS,
=
CNBSa/CNBS
(16)
where C-+ is the mol/kg of NBS- sorbed on the ODS packing and C w is the molar concentration of NBS-in the equilibrating sample solution, as above. RESULTS AND DISCUSSION Trace Conditions. Sorption isotherms of NBS- (i.e. plots of C W versus C& were measured at ionic strengths of 0.050 and 0.500 in pH 5.0 solutions that all contained 0.0200 M TBA+. This concentration of TBA+ was chosen because, with it, C m a was expected to have its largest values. The two ionic strengths were chosen because they are the smallest and largest ones used in testing the model. Both isotherms (not shown) are linear up to at least Cms = 2.5 X lo4 M (the highest concentration tested). Furthermore, examination of Figure 4 in ref 10 shows that even in the absence of TBA+ the sorption isotherms of NBS- are still linear to well above C m = 2.5 X lo4 M. Thus, regardless of the values of CmA and c, the sorption of NBS- will be occurring at trace conditions for any value of C m below 2.5 X lo4 M. Therefore, all of the model-testing experiments were performed at trace conditions, since they were performed at C, = 1.49 X 10” M. Sorption of NBS- in the Presence of TBA+. In Figure 2 are presented plots of the experimentally measured values of the distribution coefficient K m g (eq 16) versus Cmk The solid line curves were fit to the experimental points with the aid of French and Ship’s curves. Each of the five curves was measured at a different ionic strength. It is the data in Figure 2, along with the data in Figure 1, that are used to quantitatively test the double-layer sorption model for NBS-. Other than the trivial parameters 2-,F,R, and T, eq 15 contains nine parameters: KmsC,KIEX,ASP, ~ T B A ,c , d, YW, k,and p m s , If ~ C ~ ~~ and A c are specified, the values of all of the parameters in eq 15, except the two constants KIEXand pms”, are known. It thus becomes possible, at a constant value of the activity of TBA+ in solution, to perform a nonlinear least-squares fit of eq 15 to an experimentally measured plot of Kws versus c in order to obtain values of the constants K m and p m s , m . That is, at a constant amAthese two are the only adjustable parameters (unknowns) in eq 15. Details follow. Values for AsP (3.09 X lo9 cm2/kg) and d (1.0 X lo4 cm) have previously been evaluated for the system in which TBA+ is the potential-determining ion on this batch of ODS packing (IO). Values of the solution activity coefficient y m at c > 0.1 were assumed to be the same as those of p-toluenesulfonate, which are available in the literature (36);and those
2038
ANALYTICAL CHEMISTRY, VOL. 63, NO.
18, SEPTEMBER 15, 1991
Table I. Results of the Evaluation of the Data in Figure 2 at Seven Different Activities of the TBA+ Iona
-600
-400 -300
zao + "TEA9
mol/L 0.0020 0.0040 0.0060 0.0080 0.0100 0.0120 0.0140
KIEX
lrADs,NEs-
kJ/mol
ZEICO, kJ/mol
209 i 10 0.6 f 2.9 -10.2 i 0.6 0.9 i 5.8 -10.3 f 0.8 226 i 18 218 i 11 -0.1 i 1.3 -12.0 f 0.8 0.6 i 0.7 -13.5 i 0.9 216 f 8 219 i 7 1.8 f 0.6 -14.9 i 1.0 2.9 i 0.6 -15.7 i 1.1 226 i 6 4.0 i 1.1 -16.4 i 1.1 236 i 8 221 i 10 (mean)
rl",
kJ/mol
Y 0
2&
-9.6 i 3.0 -9.4 f 5.9 -12.1 i 1.5 -12.9 i 0.8 -13.1 i 1.2 -12.8 i 1.3 -12.4 i 1.6
v)
m
700 600
z
Y
500 400 300
300 ADS
Uncertainties are standard deviations from nonlinear leastsauaree curve fitting.
ionic Strength
Table 11. Comparison of Experimentally Measured Values of ICNssJ with Theoretically Calculated Values (in Parentheses) Obtained by Substitution of Klgx and p"s from Table I into Eq 15 at Seven Activities of TBA+ and Five Ionic Strengths "TBAI
mol/L 0.0020 0.0040 0.0060 0.0080 0.0100 0.0120 0.0140
C
0.050
0.070
400 (432) 324 (335) 492 (490) 420 (403) 542 (547) 460 (442) 585 (592) 487 (471) 625 (631) 509 (494) 663 (663) 528 (528) 700 (692) 541 (540)
0.100
0.300
0.500
206 (246) 263 (296) 311 (329) 345 (353) 366 (373) 379 (391) 388 (406)
100 (105) 128 (123) 145 (145) 155 (160) 161 (167) 168 (172) 171 (172)
81 (72) 95 (85) 111 (104) 121 (116) 127 (122) 132 (124) 134 (123)
at c < 0.1 were taken from the table of Kielland (37),mauming an ionic size parameter of 3.5 x lo4 cm. They varied from = 0.608at c = 0.50 to y m = 0.810 at c = 0.050. Values of $o can be calculated from the data in Figure 2 via SGC theory, as previously discussed (IO). At constant w, $o is constant. As noted above, it is desired to plot K M e vs c at constant amA. For this purpose values of rmA and Kmr at various values of c but constant %A were obtained as follows: Figures 1and 2 were both replotted as Kmc vs w and rm vs %, respectively, after converting CmA to amA by multiplying by the activity coefficient Y T B A , as previously discussed (IO). Then a t any desired amA the values of rmA and K m a were read off the new plots at all five ionic strengths. This was done at seven different values of aTBA. For each value of amA, the parameter K m , . was plotted versus c. Equation 15 was then fit to the experimental points by using the nonlinear least-squares curve-fitting program KINET(38) in order to obtain Km and pms,NBs. Presented in columns 2 and 3 of Table I are the values of these two constants, which were obtained at each of the seven aTBA. Shown in Figure 3a-d are plots of K m s versus c for four representative activities of TBA+. The points are experimental. The solid lines are the theoretical values calculated by substituting the least-squares values of K m and p m s into eq 15. Shown in Table I1 for all seven values of amA are the experimentally observed values of K m r and, in parentheses, the corresponding theoretical values from eq 15. The closeness of agreement between theory and experiment is a measure of how well the double-layer model agrees with experiment. The agreement is good. Column 4 in Table I presents the computed values of Z-F$o. The standard deviation for this term arises completely from the experimental uncertainty in q0c a l d t e d from SGC theory (IO). The sum of Z-F$,, with the least-squarea value of pis the "electrochemical potential". Its values are presented in column 5 of Table I.
(c)
Figwe 3. Dlstributkn coefficient for NBS-versus knic s t r e n p at four different activities of TBA': (A) 4.0 X 10"; (B)8.0 X 10 ; (C) 10.0 X 10"; (D) 14.0 X lo4. Square points are experimental. SdM line is theoretical from eq 15. Dashed lines are theoretical contributlons of dynamic ion exchange (eq 7) and surface adsorptlon (eq 12).
~
The standard deviations of Km at each %are only about 5% relative, which is quite small. The standard deviations of p-, on the other hand, are very large especially at I 8.0 X 1P.One reason for the large uncertainty in the fitted value of pmm is the fact that" p is much smaller than Z&o, the term to which it is added (eq 12). This is seen by comparing columns 3 and 4 in Table I. That is, the surface adsorption of NBS- is dominated by the electrostatic attraction contribution, as reflected in Z-F$.,, rather than by the chemical interaction contribution, as reflected in" p The other reason for the large uncertainty in" p is the fact that K m + in eq 15 is generally quite a bit smaller than KNBs,isx,as discussed below. The relative contributions of dynamic ion exchange and surface adsorption to the overall sorption of NBS- are most easily seen from the separate plots of K m C x and K m d as dashed lines in Figure 3a-d. Kmjexwas calculated from eq 7 by using the least-squares value of K m ,and K m , was calculated from eq 12 by using the least-squares value of p m s , m . Comparison of the dashed-line curves with the solid-line curves clearly indicates that under these conditions ion exchange in the diffuse part of the double layer is the main process responsible for sorption of NBS in the presence of the pairing-ion reagent TBA+. Surface adsorption, though never the major contributor in these experiments, makes ita greatest contribution at high ionic strength. For example for amA = 8.0 X Kmah contributes 31% to K m e at c = 0.50, while it contributes only 8% at c = 0.050. These observations are not surprising in light of previous observations on fixed-charge site (Le. nondynamic), low-capacity ion exchangers (21,22). On a low-capacityanion exchanger (Q* = 0.045mequiv/g) at c L 0.1 M,the contribution of surface adsorption of NBS- was more important than that of ion exchange (21);while on a low-capacitycation exchanger it was found that as the ion-exchange capacity was increased from 0.01 to 0.05 mequiv/g, the contribution of ion exchange to the sorption of the sample cation m-nitrobenzylammonium became more important relative to the contribution of surface adsorption (22). In the present study the dynamic ion-exchange capacity varies between 0.09 and 0.20 mequiv/g. Since these capacities are even larger than those encountered in ref 22, it is not surprising that ion exchange is more important than surface adsorption as a retention process. Panels a-d in Figure 3 reveal that at a given amA, K mja decreases markedly with increasing c while K m & decreases only slightly. The former trend results from the decrease in the ratio I ' m / c with increasing c in eq 7, as discussed in the
ANALYTICAL CHEMISTRY, VOL. 63, NO. 18, SEPTEMBER 15, I 9 9 1
Theory, and the latter trend results from the fact that, at constant a m , +, is constant and y m is the only parameter in eq 12 that changes with c. It is notable but not surprising that, at least over the rage of dynamic ion-exchange capacities involved in this work, the value of K m is essentially constant, independent of Ita mean value and standard deviation are given in Table I. Any trend that might exist in the value of pmsm with a change in aTBA in the present system is obscured by its small contribution and large standard deviation. However, speaking generally, it might be expected that if rm (or Q,J were caused to vary over a very wide range of values, which is not the case here, it would not be surprising if 1 1 . ~ ~changed. 9 , ~ This is because, as the ODS surface becomes covered with more and more adsorbed TBA+ ions, the (hydrophobic) character of the surface could change, causing the surface activity coefficient ”y in eq 13 to change. If a nonionic sample species N were being considered, instead of the ionic one NBS-,then both Km and 2-would be equal to zero and p m , would ~ be the only parameter in the numerator of the exponential term of eqs 12 and 15. Thus, for the neutral sample species N, any changes occurring in the amount of N adsorbed as a result of an increasing amount of adsorbed TBA+ would be a reflection of the changes caused in Y ~ and, consequently, in p m ~ by, ~a change in the chemical character of the ODS surface brought about by the presence of TBA+. In principle, the sorption of N could be either diminished or enhanced by the presence of an adsorbed pairing ion. It may be noted that this interpretation of pms for an adsorbed sample species is conceptually consistent with the qualitative suggestion made by Knox and Hartwick to explain the decrease in benzyl alcohol sorption on an ODS packing as the amount of sorbed octyl sulfate pairing ion was increased (6).
-.
CONCLUSION The good agreement between theoretical and experimental values of K W , ~that is evident in Table I1 and Figure 3 is interpreted as strong support for the proposed electrical double-layer model; the more so because eq 15 has only two adjustable parameters to be “fit”. The sorption of a sample ion under the conditions of ion-pair chromatography is due to both dynamic ion exchange and surface adsorption. However, if this is so why have some workers who invoke an electrical double layer obtained a reasonably good fit to their data by using an ion-exchange model while others have obtained a reasonably good fit by using a surface adsorption model? An answer to this question may be found in the presently reported study as well as in those previously reported (21, 22).
First, when +o is relatively high, either because the dynamic ion-exchange capacity is high or because the ionic strength is low, then ion exchange tends to be the dominant process. This is seen with the present system and also with the 0.054 mequiv/g cation exchanger in ref 22. Conversely, when +,, is relatively low, either because the capacity is low or the ionic strength is high, then surface adsorption tends to dominate. This is seen with the 0.0097 mequiv/g cation exchanger in ref
2037
22 and with the anion exchanger in ref 21. Second, both the ion-exchange and the surface adsorption distribution coefficients (e.g. Km,isxand KNB~,sb) increase when the ion-exchange capacity is increased at constant ionic strength, albiet according to a different functional relationship. This means that when either dynamic ion exchange or surface adsorption is distinctly dominant over the other, then it will be difficult to detect the occurrence of the other. This may be why some workers have successfully employed a dynamic ion-exchange model (11, 26, 27) while others, working at relatively low +o, have successfully employed a surface adsorption model (12-19). Registry No. NBS-, 30904-42-8; TBA+,10549-76-5.
LITERATURE CITED Ion Pa& ChrOmetogaphy: Thecxy and Bk&gkal and PhennrrccHIMcel
~
Appucebkns; Heam, M. T. W., Ed.; Marcel Dekker: New York, 1965. Knox, J. H.; Jwand, J. J . Ctuomatog*. 1978, 140, 297-312. Klssinger, P. T. Anal. chem.1977, 4S, 883. Scott,R. P. W.; Kucera, P. J . chrometog*. 1979, 175, 51-63. van de Venne, J. L. M.; Hendrikx, J. L. H. M.; Deelder, R. S.J . ChsomtOgr. 1978, 167, 1-10. K ~ xJ., H.; Hat’twlck, R. A. J . chrome-. 1981, 204, 3-21. Kraak, J. C.; Ahn, C.-X.; Fraanje, J. J . Ctwomatog*. 1981, 200, 309-376. Mlchaelis, R.; Cassldy, R. M. Adv. Ion Chrwnerogr. 1990, 2 , 21-43. , Cantwell, ~ F. F.; Puon, S. Anal. Chem. 1979, 5 1 , 023-032. Uu, H.J.; Cantwell, F. F. Anal. Chem. 1991. 63, 993-1000. Dee&, R. S.; van den Berg, J. H. M. J . Chrwnetogr. 1981, 278, 327-339. Weber, S. G.; On, J. D. J . chrometog*. 1985, 322, 433-441. Weber, S. G. Talante 1989, 36, 99-100. Stahlberg, J. J . -tog*. 1986, 356, 231-245. StaMberg, J. CtwomatograpMe 1987, 2 4 , 820-820. Stahlberg, J.; Furangen, A. chrometog*apMa 1987, 24, 783-798. Stahlberg. J.; Haggl~nd,I. AMI. chem.1988, 6 0 , 1956-1904. Bertha, A.; Vlgh, Stahlberg, J. J. chrometog.1990, 506, 85. Stahlberg, J.; Bartha, A. J . chrometog*. 1988, 456, 253-265. Del Rey, M. E.; Vera-Avlla, L. E. J . Uq. Chromatug. 1987, 10, 2911-2929. Afrashtehfar, S.; Cantwell, F. F. Anal. Chem. 1982, 54, 2422-2427. Hux, R. A.; Cantwell, F. F. Anal. Chem. 1984, 56, 1250-1203. Cantwell, F. F. In Advances in Ion Exchange and Solvent EXbgcMon; Marlnaky, J. A., Marcus, Y., Eds.; Marcel Dekker: New York, 1905 Vd. 9, Chapter 0. Cantwell, F. F. J . Pherm. Bkmed. Anal. 1984, 2 , 153-164. Overbeek, J. Th. 0. In M Scknce; Kruyt, H. R.. Ed.; Elsevler: New York, 1952 Vd. 1; Chapter 4. van der Hcuwen, 0. A. G. J.; Sorel, R. H. A,; Hulshoff, A.; Teeuwaan, J.; Indemans. A. W. M. J . Chromato@. 1981, 200, 393-404. Wu, M.J.; Pacakova, V.; Stullk, K.; Sacchetto, G. A. J. Chrometog*. 1988, 430,303-373. Hung, C. T.; Taylor, R. B. J . chrometogf. 1980, 202, 333-345. 1981, 200, 175-190. Hung, C. T.; Taylor, R. E. J. chrome-. Bertha, A.; Bllliet, H. A. H.; DeGalan, L.; Vlgh, Gy. J . chrometog*. 1984, 207, 91-102. Uu, H.J. Thesis, University of Alberta, fall 1988. Hemerich, F. Ion Exchange; McOrawH#l;New York, 1962 chapter 5. Graham, D. C. chem.Rev. 1947, 41, 441-501. Laitlnen, H. A.; Harris, W. E. ChemlcalAna@k, 2nd ed.; Mc(Law-HlN: New York, 1975; Chapter 4. May, S.; Hux, R. A.; Cantwell, F. F. Anal. Chem. 1982. 5 4 , 1279-1282. Bonner, 0. D.; Easterllng, 0. D.; West, D. L.; Holland, V. F. J . Am. Chem. Soc.1955, 77, 242-244. Kielland, J. J . Am. chem.Soc. 1937, 50, 1075-1678. Dye, J. L.; Nicely. V. A. J . Chem. Educ. 1971. 48. 443-448.
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RECEIVED for review March 25,1991.Accepted June 19,1991. This work was supported by the Natural Sciences and Engineering Research Council of Canada and by the University of Alberta.
