1820
Anal. Chem. 1801, 63, 1820-1830
Micellar Electrokinetic Capillary Chromatography of Acidic Solutes: Migration Behavior and Optimization Strategies Morteza G. Khaledi,* Scott C. Smith,' and Joost K. Strasters Department of Chemistry, North Carolina State University, Box 8204, Raleigh, North Carolina 27695-8204
Mlceiiar ekctroklnetic capillary chromatography (MECC) is sultabie for the separation of mixtures of uncharged and charged solutes. I n this paper, the migration behavior of acldk compounds In MECC Is quantltatlvely deedbed in terms of different modeis. These equations describe the reiatlonshlps between the two migration parameters in MECC (retention factor and mobility) and the two important experimental parametem (pH and mkMe cowenbath) that have a great Influence on the mlgration behavlor and selectivity. Interestingly, the moblilty and retention factor of a given 80lute could behave differently wlth the varlations in pH. This woukl rake a questbn of whlch parameter actudly represents the migration behavior of a solute in MECC retention factor (a chromatographlc parameter) or mobility (an eiectrophoretlc parameter). The consequences of miceiiar-mediated shifts of ionizatlon constants on selectlvlty and optlmization strategies in MECC are dkussed. The mathematical models would allow the prediction of migration behavior of solutes based on a limited number of initial experiments. TMs would greatly facilllate the method development and optknization of separatbns of knlrabte aq"dsby MECC and, In addnkn, important phyrlcal and chemlcal characterlstlcs of solutes such as thdr apparent ionlzath constants in micellar media and thdr pmWon COeMcknkr into mlcdke (over a wkk range pH values) can be determtnud. The mockls were vertfied, as good agreements were observed between the predlcted and the experlmentally observed migration behavior. Based on the preihnlnary results, the pH and micdk concentration are likely to be interactive parameters in many situations. As a result, simultaneous optimization of these two parameters would be the most effective strategy to enhance the MECC separation of acldlc solutes.
INTRODUCTION Micellar electrokinetic capillary chromatography (MECC) has extended the enormous power of capillary zone electrophoresis (CZE) to the separation of uncharged solutes (1,2). The high efficiency of CZE is often adequate to separate charged compounds with very small differences in mobility ( 3 , 4 ) ;therefore, one must have compelling reasons in order to use micelles in a CZE system for the separation of charged compounds. Micelles provide both ionic and hydrophobic sites of interaction simultaneously, making MECC preferable to CZE for the separation of mixtures of charged and uncharged solutes. Another application is the separation of charged solutes with identical electrophoretic mobilities (5). The question is whether micelles (or other forms of organized media) would provide the additional selectivity needed for the separation of compounds of this nature (5). In order to address these issues for a broad range of ionizable compounds, one has to achieve an in-depth understanding of the migration 'Present address: M ellan Laboratories, Inc., P.O.Box 13341, Research Triangle P a r k 3C 27709. 0003-2700/91/0363-1820$02.50/0
behavior of acidic and basic solutes in MECC as well as the exact role of important parameters that have the greatest effects on migration and selectivity in this system. A fundamental study of the migration mechanism would lead to a priori prediction of retention behavior based on a limited number of initial experiments. As a result, one could take full advantage of an additional selectivity that the use of micelles or other organized media might provide in different applications. This would greatly facilitate the development of effective MECC separation methods. Otherwise, the method development and optimization of a separation would be based on trial and error or the researchers experience and intuition (6). Since the first description of MECC by Terabe and coworkers, a large number of applications (for neutral and charged solutes) have been reported in the literature (7-11). However, a good assessment of the capabilities of MECC for the separation of ionizable compounds requires a more systematic study of the migration behavior. A more formalized and quantitative description of the retention behavior in MECC will be beneficial for two apparent reasons. First, in method development, the retention behavior of a solute under different experimental conditions can be predicted on the basis of a limited number of experiments, thus facilitating the optimization of retention and selectivity in practical separations. The migration behavior of ionizable compounds in MECC is far more complicated than uncharged compounds. As a result, more than one parameter (e.g., micelle concentration, pH, etc.) should be incorporated in the optimization strategy in order to achieve an adequate separation of complex mixtures. Often, these important parameters are interactive in nature. This means that a simultaneous, multiparameter optimization strategy should be selected in order to achieve an effective separation. An optimization procedure based on a retention model would serve this purpose. Second, from the retention behavior of the solutes, further conclusions with respect to the physical and chemical properties such as apparent ionization constants in micellar media and the extent of solute association with micelles can be drawn. In addition, information on the characteristic values of a micellar system such as critical micelle concentration (cmc) can be derived. An extensive investigation of the migration mechanism of ionizable compounds in MECC has been initiated in this laboratory. In this paper, different models are presented to quantitatively describe the migration behavior of acidic compounds in an MECC system with anionic micelles (sodium dodecyl sulfate, SDS). The migration behavior of cationic solutes and the use of these models on the optimization of separation will be described in separate communications (12, 13).
THEORY Two important parameters that greatly influence the migration behavior of acidic solutes are pH and micelle concentration. The models derived in the following describe the @ 199 1 Amerlcan Chemical Society
ANALYTICAL CHEMISTRY, VOL. 63,NO. 17, SEPTEMBER 1, l 9 Q l 1821
Flguro 1.
A-
Interaction of a neutral solute (n) wlth a micelle (mc) in
MECC.
effect of these two parameters on capacity factor ( k ’ ) and electrophoretic mobility G)of acidic compounds in an MECC system with anionic micelles. For the derivation of the models for acidic compounds, a phenomenological approach was used. This approach, which has been previously reported for HPLC as well as MECC (14-1 3, assumes that the net migration parameter of an acidic solute (k’,P, or velocity) is the weighted average of the migration parameter of the solute in the undissociated and dissociated forms in micelles and in the bulk solvent. k‘ vs [SDS]. Uncharged Solutes. Terabe et al. have already reported the retention model for uncharged solutes (I, 2). For comparative purposes and for the sake of completeness, the equation for neutral compounds was derived by using the phenomenological approach. Figure 1presents the typical migration behavior of a neutral solute in MECC. The electrophoretic mobility of a neutral solute in MECC, pn, is proportional to the mobility of the micellar phase, pmc: Pn =
[
&]Pmc
Since the retention factor, k’, is defined as the ratio of the amount of solute associated with micelles to that in the aqueous phase, the term k ’ / ( k ’ + 1) represents the mole fraction of the solute in micellar pseudophase. Equation 1 can also be expressed as
The electrophoretic mobility of a solute is related to the retention time by
where L,is the total length of the capillary, L,is the distance from the upstream end to the detector, and V is the applied voltage. Substituting retention times for the mobilities, one would arrive at the equation that was originally reported by Terabe et al. (1):
Anions and Acidic Solutes. The migration behavior of a weak acid (and for an anion) is shown schematically in Figure 2. Note that an anionic solute is a special case of an acid that is fully dissociated. In contrast to uncharged solutes, not all retention of anions is explained by interactions with the micellar pseudophase, since these compounds have a negative electrophoretic mobility in the aqueous phase. Therefore, in MECC, the mobility of an anion would be the weighted average of the mobility of the micellar phase and ita own mobility in the aqueousphase. This can be accounted for by including the observed overall mobility in the absence of micelles, po, in eq 1:
c
Flgure 2. Interaction of an acidic solute acidlbase pair (Awith a micelle (mc)in MECC.
-
HA)
As shown in Figure 2, two migrating fractions can be discenred: the acid/conjugated base pairs associated with the micelles and migrate at a mobility of hc; the anionic (dissociated)form in the aqueous phase moving at a mobility of P,,. Another important migration mechanism is through the electroosmotic flow. All equations, however, are expressed in terms of electrophoretic mobilities (eq 3a) because the electroosmotic mobility, pea, is constant for all components in the system. It is important to note that, in deriving these equations, several assumptions have been made; for example, it is assumed that the mobility of micelles is not altered when associated with analyte, that secondary chemical equilibria with buffer componentsdo not occur, and that the possible effects of the ionizable analytes and their equilibria on the {potential and hence electroosmotic flow are insignificant. From eq 4, one can derive the following equations: P - Po k’= Pmc - P
,
I
and
where tois the retention time in the absence of micelles. A similar equation has been reported in the literature in terms of velocity rather than mobility: however, it was not verified experimentally (17). The retention factor in MECC is directly proportional to the micelle concentration as described by Terabe et al. (1) through the following equation: k’ = Pmwv[S]- cmc) (6) where PmW is the partition coefficient of solute into micelles, V is the molar volume of the surfactant, and [SI is the total surfactant concentration. This equation is valid at low micelle concentrations. It is important to note that eq 6 is valid for both ionizable (acidic) and uncharged solutes. The main difference between the uncharged and acidic solutes is that the Pmwfor acidic solutes is a function of the pH of the medium as described below. k’vs pH. The retention factor of an acid is the weighted average of the retention factor of its undissociated (HA) and dissociated (A-) forms as
k ’= F89HAk ’HA + PqA-k 2-
(7) where k jIA and k ’A- are the limiting retention factors of the acid in the associated and the dissociated forms, respectively. The F values are the mole fractions of the acid in the associated and dissociatedforms in aqueous solution and are equal to
and
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ANALYTICAL CHEMISTRY, VOL. 83, NO. 17, SEPTEMBER 1, 1991
Substituting eqs 8a and 8b into eq 7 would result in the final equation
k’=
k’HA
+ ki-K/[H+I)
(9)
1 + Ke/ [H+I It is interesting to note that eq 9 has exactly the same format as that of the HPLC techniques (14-16). P,, VB pH. According to eq 9, the variations of the retention factor of acidic solutes as a function of pH are a sigmoidal relationship. Since k’ is directly related to the solute’s partition coefficients into micelles, P,, it is important to explore the dependence of P, on pH. The Pmw is defined as
(16) where [MI is [SI - cmc. Therefore, the mole fraction of an acidic solute is a function of its binding constant (K,) to micelles, the micelle concentration, and the pH. Similar equations can be derived for P A - and PqA-: PA- =
(K”’A-[Ml)(Ka/[H+])
T
(17)
where Tis the denominator of eq 16. Substituting for the F values in eq 14, the following equation would result: Substituting Pw[HAlrq for [HA],, PA-[A-], for [A-I,, and
K,/ [H+] for [A-]/ [HA], the following equation can be derived:
Again PHI,and PA-are the limiting partition coefficients of the associated and dissociated forms of the acid from the aqueous phase into micelles. Note that eq l l a could also be derived by substituting eqs 8a and 8b into the following relationship:
Since the apparent dissociation constant in micellar solutions, Ka,epp,is defined as
w vs pH and [MI.In a CZE system (in the absence of
Tmay be simplified to (1 + Kwpp/[H+])(l P m [ M ] ) and one would arrive at a final equation
micelles), the electrophoretic mobility of an acid can be expressed as
where is the net mobility of the solute and PA- is the mobility of the fully dissociated anion. This equation can then be rewritten as (13) The net electrophoretic mobility of an acidic solute in an MECC system can also be quantitatively described through the phenomenological approach as following:
= P H A p m c + PA-p’qA-
This equation directly shows the relationship between mobility and the two important parameters, pH and [MI, that have a great influence on the migration behavior. It can be simplified by defining the two limiting mobility terms, p~ and pA-,in micellar media as
+
(14) where p is the net mobility of an acidic solute, pmcis the mobility of micelles, and pA- is the mobility of A- in the aqueous solution; F values with the subscripts or superscripts HA, A-, mc, and aq represent the mole fraction of solute in the protonabd and dissociated forms in micelles and water, respectively. T h j s equation presents a similar concept as eq 4; that is; the solute’s mobility is a weighted average of the mobility or the dissociated form in aqueous solution plus the mobility of a fraction of HA and A- that moves with micelles. In the protonated form (HA), the solute’s mobility is a function of its interaction with micelles ( P w m c ) and , in the dissociated form (A-), the solute’s mobility is a result of its aqueous One can mobility (PA-pA-)and micellar mobility (PA+,,). define as [HA], (15) PHA = WAIm + W l e q + [A-lm + [A-leq p
+
Substituting KmHA[HAIaq[M] for [HA],, PA-[A-],[MI for [A-I,, and [HAI,,K,/[H+] for [A-1, would result in the following equation:
and
Then, eq 21 could be further simplified to
+
PHA
P =
[H+l)
1 + (Ke,app/[H+I)
(24)
EXPERIMENTAL SECTION Apparatus. Experimente were carried out on two laboratory-built CE systems (18). Both systems use a 0-30-kV high-voltage power supply (Series EH, Glassman High Voltage, Inc., White-
house Station, NJ), a variable-wavelength UV detector (Model 200, Linear Instruments, Reno, NV) operating at 210 nm, and 50-pm-i.d., 375-rm-0.d. fused silica capillary tubing (Polymicro Technologies,Phoenix, AZ). The total length of the capillarywas 40 cm, and detection was performed 26.5 cm downstream. The capillary temperature was maintained at 40 O C by jacketing in light mineral oil by using a constant-temperaturerecirculator (Type K2-R, Lauda,Germany). Electropherograms were recorded
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ANALYTICAL CHEMISTRY, VOL. 63,NO. 17, SEPTEMBER 1, 1991 c P
IC
c
9 9
I I
N W
idLI
I
0
1
2
3
Retention time, minutes
4
0
1
2
3
4
0
Retention time, minutes
2
1
3
4
Retention time, minutes
1
0
2
3
4
Retention time, minutes
Figure 3. Effect of rinsing on reproducibility of a test mixture. Conditions: 50 mM phosphate buffer, pH 7; 10 mM SDS; 15 kV; L, = 40 cm, L , = 26.5 em. 1 = arterenol; 2 = 2CP 3 = 23CP 4 = 2,4,6trlmethylbenzoic acid; 5 = phydroxybenzolc acid; 6 = "ethylbenzdc acid: 7 245CP. (a, left) Run 1, hmediatdy after rinsing; (b, left middle) run 20; no rinsing was done before runs 2-20: (c, rlgM mkldle) run 21, after rinsing before run; (d, right) run 30; capHlary was rinsed before each run for 21-30.
--
with an electronic integrator (Model SP4200, Spectra-Physics, San Jose, CA, or Model QA-1, Waters Associates, Milford, PA). Total current was recorded on a strip-chart recorder by measuring the voltage across a 1-kQresistor in series with and downstream of the capillary. hagents and Chemicals. Chlorinated phenols were selected as the test compounds based on three factors: water solubility, W absorptivity, and favorable acid dissociation constants. The mono-, di-, tri-, and penta-substituted chlorophenols (CP's) selected are 2- (ZCP), 3- (3CP), and 4-chlorophenol (4CP), 2,3(23CP), 2,4- (24CP),2,s (25CP), and 3,5dfichlorophenol(35CP), 2,4,5- (245CP) and 2,4,64richlorophenol (246CP), and pentachlorophenol (pentaCP) (Aldrich Chemical Co., Milwaukee, WI). Tetrasodium pyrophosphate (Fisher, Raleigh, NC) was selected as the buffer, and sodium dodecyl sulfate (SDS Sigma, St. Louis, MO) was the surfactant. The disturbancein the electropherogram baseline from HPLC-grade methanol (Fisher) was used as the neutral marker, while Sudan III (Aldrich)was used as the indicator for measuring micelle mobility. Procedure. All experimentswere performed with 50 mM ionic strength pyrophosphate over the pH range 5-11. When present, the surfactant concentration for the pH study was 20 mM. The applied voltage, 18 kV,was selected in order to keep the total current between 50 to 60 pA. The typical sample contained approximately 0.1 mg of each chlorophenol to be teated and 0.1-0.2 mL of Sudan III-eaturated methanol in enough buffer to make the total volume 2 mL. Injection was done by gravity; the upstream end of the capillary was placed in the sample vial, which was then raised approximately 5 cm for 5-20 s. At the start of each day's experiments,the capillary wm flushed continuously for about 30 min. Flushing was performed by applying vacuum from a water aspirator to the sealed downstream buffer flask. When not under vacuum, the flask was open to air. The capillary was rinsed with buffer for 30 s before each run. Rinsing procedures have been discussed by other researchers with mixed conclusions (19-24). In this laboratory, we examined the influence of several operating parameters on the reproducibility of the retention time and mobility of a test mixture composed of chlorophenols, benzoic acids, and a catecholamine. The significanceof rinsing is illustrated in Figure 3. Without rinsing between injections, the retention behavior of solutes may change
r
I
I
I 0
0.01
0.02
0.03
0.04
0.05
0.06
ISDSI (MI Flgure 4. RelatlonsMp between k'and [SDS] for the neutral solutes 2mphthd (W tokrene (*I. nitrobenzene (01,phenol (A),and " I (0).
with increasing run number. Figure 3a is from the first run after rising the capillarywith buffer. Figure 3b was taken aftar 20 runs; no rinsing was performed between runs. Notice that the retention times of all components have shifted, the relative positions of components are different, and 245CP has shifted from the seventh position to the fourth. Upon rinsingfor 30 8, the retantion time were restored to their original values (Figure 3c). After 10 runs with rinsing between each run,the retention times show little change (Figure 3d). In addition, the peak heights appear to be more reproducible. The details of this reproducibility study will be published elsewhere
(%I.
Calculations. Elution times were compiled and mobilitieswere calculated in spreadsheet format by using Quattro Pro (Borland International, Inc., Scotts Valley, CA) on a 80286-microprocessor-based PC (Compaq Deskpro 286, Austing, TX). Weighted linear regression was also preformed in spreadsheet format following standard procedures (26).Weighted nonlinear regression was performed by using the Marquardt method in SAS software (Cary, NC) operating on an 80386-microprocessor-basedPC (Northgate 386 Super Micro, Plymouth, MN). RESULTS AND DISCUSSION k' vs [MI. Terabe et al. have shown that, for neutral solutes, the retention factor in first approximation is linearly
1824
ANALYTICAL CHEMISTRY, VOL. 63,NO. 17, SEPTEMBER 1, 1991
Table I. P, of Neutral Solutes from the Slopes of k'vs [SDS] As Shown in Figure 4
l 800
o
o
o
L
P,W
solute
lit. ( 1 )
Figure 4
\
\.
600-
resorcinol phenol nitrobenzene toluene 2-naphthol
22
19
52 135 318
49 131 305
656
720
&z
\
-
-\
400\.
\.
\
200.
0, 5
6
7
8
9
10
I
PH .I'
,....'
,.0'
I../
.....D_
* ,,(,....'..." ....'
_--__---
t
0
I
0.01
0.02
0.03
0.04
0.05
0.06
w
e 5. RelatknsMp between k'and [SDS] wkh correction for solute mobllity in the absence of micelles for 2CP (O), 3CP (A),23CP (0), 25CP ('), 245CP (m), 248CP (A),and pentaCP (0).
related to the micelle concentration through eq 6. Figure 4 shows the linear relationship between k ' and the total surfactant concentration for several neutral compounds. As shown, all lines almost pass through the same intercept (equal to cmc; 0.004 M), and the slope of the line (PmW) increases with the hydrophobicity of the compound. This value is smaller than the frequently reported literature cmc value of 0.008 M (in pure water and a t 25 "C). This is due to the presence of buffer and consequently higher ionic strength as well as higher operating temperatures in this study. There is good agreement between the P,, values measured by MECC and those reported in the literature. The data presented in Figure 4 and Table I demonstrate that the relationship in eq 3 is accurate for our test solutes. As mentioned previously, the original form of this model (eq 3) was experimentally verified by Terabe and co-workers ( 1 , 2 ) . The linear relationship between k 'and [SIis also valid for ionic solutes (both anionic and cationic). The major difference between the ionic and nonionic compounds would be in the relationship between k 'and different mobilities (i.e., eq 5b) and the fact that for ionizable compounds P,, is a function of pH (eq 11). The retention factors of the acidic solutes were calculated according to eqs 5a and 5b. The similarity between eq 2 (k' for neutral solutes) and eq 5a (k' for acidic solutes is interesting. The only difference between these two equations is that for acidic solutes the electrophoretic mobility of the dissociated acid in the aqueous phase has to be taken into account for the k 'calculations. For example, Figure 5 shows the k 'vs [SJ plot for a group of acidic compounds (chlorinated phenols) using the corrected model (eq 5a). (Recall that the corrected model takes the aqueous mobility of the solute, p,,, into account.) As shown, all lines pass through the same origin (cmc). When the same experiment was conducted by using the uncorrected model, there were widespread intercept values for different compounds. It should be noted that a linear behavior was observed for the uncorrected model (eq 2). This linear behavior is probably due to the variations in t,, with surfactant concentration in the denominator of eq 2. Note that since the other criteria (Le., same intercept for all compounds and correct P,, values) are not met, eq 2 is not a good model for acidic solutes. As mentioned above, a form of eq 5b was previously reported by Otsuka et al. for substituted
Flguro 6. Dependence of the micelle-water partition coefficient (P,) on pH for 4CP (-), 35CP (---), and 245CP (-.-).
phenols but was not experimentally verified (17). The following P,, values were observed for the acidic solutes at pH 7.0 using the corrected model (eq 5a): 2CP, 116; 3CP, 175; 23CP, 380; 25CP, 292; 245CP, 766; 246CP, 159; and pentaCP, 145. For 2CP and 3CP, the two P,, values determined from eqs 2 and 5a were almost identical because at pH 7 both of these compounds are nearly protonated in micellar solution and therefore their is almost zero. The corrected PmW values for other compounds were all smaller than the uncorrected values (using eq 2). This is expected because these solutes are partly dissociated at this pH, and due to the electrostatic repulsion between the dissociated acid and the anionic surfactant, the P, values are smaller as compared to the protonated form. As shown in eq 11,the p, of an acid decreases with an increase in pH (i.e., increase in dissociation), which is also shown in Figure 6. This would then result in a decrease in retention factor according to eq 6. The dependence of the slope of k 'vs [SDS]on pH was studied for toluene (a neutral solute) and two weak acids (23CP and 245CP). As expected, the pH does not have any influence on the k 'vs [SDS] plot remains for a neutral compound such as toluene because PmW constant regardless of pH. For the two chlorophenols, however, the variations of k 'with micelle concentration decrease as the pH increases, which again indicates a decrease of P,, at higher pH values. For trichlorophenol, the slope of the lines at pH 8 and 9 is the same. This shows that at pH 8 this molecule is completely ionized and a further increase in pH would not have any effect on k'. Fitting the Models. The migration behavior of acidic solutes in CZE and MECC is greatly affected by the pH of the buffer as shown by eqs 9,13, and 24. These equations predict a sigmoidal relationship between both mobility and retention fador with the pH. The migration of the chlorinated phenols was studied within the pH range of 5-11 in the absence (CZE system) and the presence of micelles. The data were fit to the three models (eqs 9, 13, and 24) by using a weighted nonlinear (WNLIN) regression of the models and a weighted linear (WLIN) regression of the linearized models as described below. An estimate of the optimum values for the limiting mobilities and retention factors (i.e., for HA and A-) as well as the pK, values was obtained. The WNLIN regression method calculates the optimum parameter values by minimizing the x2 function with respect to each of the parameters simultaneously (27). In other words, the procedure optimizes the parameters in order to obtain the least-errors sum of squares in predicting the F or k'. After the WNLIN procedure, the calculated parameter values can be used to estimate the I.C or k 'values at the various pHs and compared with the measured values. The estimated parameters from the WNLIN method of eqs 9,13, and 24 for the CZE and MECC experiments are listed in Tables 11-IV.
ANALYTICAL CHEMISTRY, VOL. 63,NO. 17, SEPTEMBER 1, 1991
Table 11. Estimates of PA- and pK, by Weighted Nonlinear Regression and Weighted Linear Regression of Data from CZE Experiments' WNLIN
a Using
-23.92 -22.40 -20.71 -21.94 -22.53 -21.72 -20.88 eq
-5
WLIN
PK.
PA-
2CP 3CP 4CP 24CP 25CP 35CP 245CP
1825
PK.
PA-
f 0.58 8.20 f 0.03 -22.61 f 0.29 8.16 f 0.02
f 0.99 f 0.23 f 0.21 f 0.21 f 0.51 f 0.26
8.83 f 0.04 8.83 f 0.05 7.56 f 0.01 7.18 f 0.01 7.79 f 0.02 6.71 f 0.02
-21.74 -20.60 -21.31 -22.18 -21.31 -20.52
f 0.02 f 0.08 f 0.86 f 0.45 f 0.48 f 0.48
8.74 f 0.04 8.80 f 0.05 7.54 f 0.01 7.17 f 0.01 7.79 f 0.01 6.68 f 0.06
a -20 -
-3 0 4
5
6 2
8
7
95
1
0
1
1
1 x 2
9.
For the CZE experiments,the fit is good for all the compounds as evidenced from the data shown in Figure 7 (WNLIN fit). The estimated pK, from the WNLIN of the model (eq 13) is very close to those reported in the literature for all the compounds. In fact, the difference in pK,(CZE) and pK,(literature) is almost constant and ranges between 0.2 and 0.46 unit with an average of 0.31 f 0.09 for nine chlorophenols. Note that it is expected that the pK, values measured by CZE in this work be different from those reported in the literature (which were probably measured potentiometrically) since the experimental conditions (ionic strength, temperature) are different. The fit for the mobility vs pH model in MECC is good for the monochlorophenols. The resulta deteriorate for the di- and trichlorophenols (Figure 8, W"fit). This same observation is made when the data are examined by WLIN. The main reason behind this is that the variation in the net mobility of these hydrophobic phenols with pH in the MECC is small. In other words, the difference in mobility of the associated and dissociated forms of the di- and trichlorophenols is relatively small. In fact, for some solutes such as 25CP, there is hardly any difference between the two limiting mobilities. As a result, the nonlinear regression of the data with a narrow range of variation would not provide a good fit. This problem is magnified by the increase in experimental
PH Flgure 7. Dependence of mobility on pH in the absence of surfactant for 4CP (0),35CP (-), and 245CP (X) using weighted nonlinear regression. Lines represent the predicted behavior according to eq 13 and presented in Table 11. Symbols represent the average mobilities.
-5 -10-
l
>
E
SL
-15-
a -20-25
-
a
30 5
4
6
6
7
9
1
0
1
1
1
2
PH Figure 8. Dependence of mobility on pH in the presence of 20 mM SDS for 4CP (0),35CP (-), and 245CP (X) using weighted nonlinear regression. Lines represent the predicted behavior according to eq 24 and presented in Table 111. Symbols represent the average mobilities.
Table 111. Estimates of BHA, pA-, and pK, by Weight Nonlinear Regression and Weighted Linear Regression of Mobility Data from MECC Experiments at 20 mM SDSa WLTN
WNLIN 2CP 3CP 4CP 24CP 25CPb 35CP 245CP
-11.82 -13.97 -13.98 -22.55 -21.76 -24.88 -25.58
f 0.18 f 0.13 f 0.13 f 0.34 f 0.36 f 0.41 f 0.67
PKWP
PA-
FHA
-22.53 -22.28 -21.57 -21.25 -22.06 -21.21 -20.53
f 0.15 f 0.14 f 0.13 f 0.18
f 0.10 f 0.18
f 0.19
,
7.93 f 0.05 8.67 f 0.08 9.13 f 0.07 7.89 f 0.68 9.12 f 3.84 9.83 f 0.21 7.43 f 0.21
PHA
-12.53 -14.16 -13.73 -22.64 -22.26 -25.08 -26.42
f 0.58
f 0.34 f 0.19 f 0.63 f 0.51 f 0.54 f 0.30
PA-
-22.60 -22.07 -21.24 -21.10 -22.03 -21.36 -20.56
f 0.12 f 0.08
f 0.13 f 0.18 f 0.19 f 0.19 f 0.18
PKa,, 8.38 f 0.79 8.98 f 1.87 9.02 f 1.19 8.07 f 0.44 7.68 f 0.14 8.45 f 0.88 7.51 f 0.33
Using eq 13. WNLIN failed to converge.
Table IV. Estimates of k", kL-,and pK, by Weighted Nonlinear Regression and Weighted Linear Regression of Capacity Factor Data from MECC Experiments at 20 mM SDS"
2CP 3CP 4CP 24CP 25CP 35CP 245CP a Using
eq 24.
k'm
WNLIN k i-
PK,
0.63 f 0.01 0.79 f 0.01 0.79 f 0.03 2.88 f 0.10 3.81 f 0.21 4.65 f 0.09 5.54 f 0.60
-0.01 f 0.04 0.05 f 0.03 0.07 f 0.02 -0.03 f 0.03 -0.03 f 0.02 -0.01 f 0.01 -0.03 f 0.02
8.59 f 0.12 8.92 f 0.11 8.60 f 0.10 7.31 f 0.04 6.75 f 0.05 7.36 f 0.02 6.62 f 0.08
WLIN
"k 0.63 f 0.45 0.79 f 0.03 0.78 f 0.04 3.60 f 0.79 3.94 f 0.96 4.64 f 0.07
k 'A-
PK
-0.01 f 0.02 0.07 f 0.03 0.07 f 0.01 0.01 f 0.04 -0.01 f 0.02 0.20 f 0.03
8.65 f 0.44 8.94 f 0.03 8.75 f 0.03 7.10 f 0.10 6.72 f 0.11 7.37 f 0.01
1828
ANALYTICAL CHEMISTRY, VOL. 63, NO. 17, SEPTEMBER 1, 1991
0
-1 5
6
7
S
9
10
11
J S
7
6
PH
Figure Q, Variation of K,/[H+] wlth pH for pK, = 6-1 1.
uncertainties at lower pH values where the mobility of the protonated hydrophobic chlorophenols approaches that of the micelles. Note that the suitable pH range for a good fit would not be the same for all solutes. One of the important factors in these equations is the term K,/[H+]. If this term is large, the anionic parameters are determined accurately, but the contribution of the protonated parameters will be negligible. The reverse holds when this value is small. An obvious physical interpretation is that a high value of K,/[H+] corresponds with a high concentration of the anionic species. The retention will be largely determined by the anionics, and thus, the corresponding parameters can be determined. This is illustrated in Figure 9, showing the value of K,/[H+] as a function of the pH and the pK, of the solute. The conclusion is that the pK, determines the region we must consider when fitting the equation; i.e., for acidic solutes (low pK,), we must consider a lower pH range in order to estimate both the protonated and the dissociated parameters. Such is the case for the di-, tri-, and pentachlorophenols. The reverse holds for less acidic species. If the fitting procedure is performed using a limited number of pH values, either the protonated or dissociated parameters will be more related to the observed experimental error in the measured values ( p or k’) than to a physical interpretation of the observed retention behavior. Unfortunately, the reproducibility of experiments in MECC begins to deteriorate at pH 7 and is significant at pH less than 6. The poor reproducibility at lower pH has also been reported for neutral compounds, which perhaps indicates that the problem stems from the electroosmotic flow (28). The electroosmotic mobility strongly decreases at lower pH values. This strong dependence of p, on pH is undesirable since any small shift in the pH would lead to large variations in pea. As a result, appropriate buffering of the solution is important. Note that the acid dissociation constants are a function of temperature; however, effective control of temperature in a CZE experiment is not quite feasible. Another problem in MECC is that the p, decreases with the pH to a point that it is no longer larger than pmc. As a result, the direction of the micelle movement would change toward the positive electrode. Otsuka and Terabe observed that at pH 5 the p, is completely balanced by pmo which results in a net zero velocity (28). Below pH 5, p, < pmcand therefore micelles move toward the positive electrode. As a result of these different factors, the practical pH range for reproducible separation in a reasonable time period is above pH 6 or 7 for the untreated silica capillaries. In contrast to the mobility model, the retention factor model in MECC gave reasonably good fits for the same set of compounds (Figure 10, WLIN fit). This is interesting since the k’values were basically calculated from the mobility data using eq 5. This, as well as the good fits obtained for the CZE experiments, rules out the experimental uncertainties in the
9
10
11
,
PH
Figure 10. Dependence of k’on pH In the presence of 20 mM SDS for 4CP (0).35CP (-), and 245CP (X) using welghted llneer regret+ sion. Lines represent the predicted behavior according to eq 9 and presented in Table IV. Symbols represent the average mobilities.
lower pH range being the reason behind the anomalous p vs pH results. One can therefore conclude that the main reason is the limited variations in mobility with pH in MECC as mentioned above. In the following section, the differences between the k’ and p variations with the pH is discussed. Linear Models. Weighted linear regression can also be used to calculate the parameters from the linear models of eqs 9,13, and 24. For CZE (eq 13), the model can be rewritten as
A plot of l / p vs [H+] is linear, and pA- and K, values can be calculated from the slope and the intercept. The mobility model in MECC (eq 24) can be linearized as
If the pKwpp is known, a plot of the left-hand side of the equation vs [H+] would be linear and the limiting values of p m and pA- can be measured from the slope and the intercept. In this work, however, we assumed that the pKwpp is not readily available and pA- can be measured experimentally. In that case, the following iterative procedure can be used with the linear model to estimate p m and pKFirst, a starting value was assumed for the pKwp and a corresponding value was estimated for pLHAfrom the slope of the linear model described in eq 26. p m and pA- were then used in eqs 22 and 23 to calculate P m and P A - . By using these K, values, a new pKwpp value was calculated from eq 20 by using the aqueous pK, value from the CZE experiment (Table 11)at a given micelle concentration. The new pK- was used as the estimated pKrqapp in the second iteration. This process was repeated until good agreement between the pKvalues calculated from the linear model and from the KaLPPmodel was obtained. For the k’model in MECC (eq 24), the linear model would be
1
1
k’ = k’m - +
[2][ &]
(27)
It was assumed that k 2- = 0, which, based on the experimental observations, is a reasonable assumption for the compounds used in this study. The weighted linear regression of the model would provide the K, and k ’m values from the slope and the intercept. The results of the WLIN and WNLIN regression of the linear models (eqs 9, 13, and 24) are listed in Tables 11-IV.
ANALYTICAL CHEMISTRY, VOL. 63,NO. 17, SEPTEWER 1, 1991
There is good agreement between the WLIN and WNLIN results. It is important that the regression procedure requires minimum knowledge of the different physical and chemical characteristics of the solutes (e.g., ionization constants and partition Coefficients). The regression procedures described in this work only utilize the migration parameter ( p , k') vs the experimental variables (pH, [SDS]). In fact, one should be cautious in using the tabulated values for ionization constants and partition coefficients in these models to predict the migration behavior simply because of the different experimental conditions (temperature and ionic strength) under which these values were derived. Interestingly, in both regression techniques, the estimatedparameters (%., pK,) might even differ greatly from the "true* values; however, the use of the estimated parameters in the model from which they were derived provides the best prediction. The accuracy of calculated parameters would depend on the accuracy of the experimental data and the model and the precision of the measured data, as well as the pH range. The WNLIN regression procedure requires the starting value specifications for the parameters in order to start the iterative algorithm to search the parameter space for the optimum values. The outcome of the WNLIN regression would depend on the selected initial values for the parameters. In this work, the starting values for the limiting mobilities and retention factors were chosen based on corresponding measured values at pH 6 and 11. The pK, values were selected based on the available values in aqueous solution. This arrangement seemed to work effectively. The procedure seemed to be quite robust, as reasonable variations in the starting parameters' values did not influence the results. It should be noted that one of the difficulties of such a search is the possibility of the existence of more than one local minimum for the x2 within a reasonable range of values for the parameters. In such a case, a coarse grid mapping of the parameter space to locate the global optimum would be advantageous (27). Migration Parameters in MECC: p vs 1% The migration behavior of ionizable solutes in MECC can be expressed in terms of the retention factor or mobility. For all solutes, the retention factor decreased with an increase in pH, Le., ktm > kj;,as shown in the sigmoidal curves in Figure 10. This is expected since the protonated acid (HA), which is the dominant form at the lower pH values, interacts to a greater extent with micelles aa compared to the dissociated form (A-), which is electrostaticallyrepelled from the micelles and therefore has a smaller partition coefficient into micelles than the protonated form. The relative fractions of the four solute species have been calculated from eqs 16-18 for 4CP and 245CP and are illustrated in parts a and b of Figure 11, showing the dominance of HA species at lower pH and Aspecies at higher pH. Unlike k', the trend of variations of p in micellar medii with the pH depends on the type of solute (Figure 8). For example, for monochlorophenols, the mobility increases with an increase in the pH, i.e., p m < 1.11;. For the tri- and pentachlorophenols, the trend is reversed; that is, the solute mobility for the more hydrophobic compounds decreases with an increase in pH, pm > pA-. This is shown in Figure 9 for 4CP, 35CP, and 245CP. For all three compounds, the trend for k'vs pH is the same while that for p vs pH is different. Note that since all the mobility values are negative (which shows solute's movement in the opposite direction of the electroosmoticflow), an apparent "decrease" shown in Figure 9 is actually an increase in mobility to the more negative values. The different behavior in mobility can be explained by examining the relationship shown in eq 14. At the low pH values, the first term dominates and p = p m = P&. The
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Figure 11. Dependence of the relative fractions of the four solute species of (a, top) 4CP and (b, top middle) 245CP on pH for HA,,, (..e), HA, (---I, and A-, (---) and the dependence of the product of relative fraction (*) mobility of (c, bottom middle) 4CP and (d, bottom) 245CP on pH for A-+eq (-.-), and total (-).
e),
contribution of the second and the third terms to the overall mobility increases with the pH, and at high pH values, p = PA- = P ~ A+- ~ PA-^. A - The contribution of the third term is probably not significant due to the electrostatic repulsion of the dissociated solute from the anionic micelles, which results in small PAvalues. Therefore, the trend of the vs pH curve is determined by the terms Pw,and PqA-pA-. The mobility of micelles is larger than any of the test solutes;
1828
ANALYTICAL CHEMISTRY, VOL. 63,NO. 17, SEPTEMBER 1, 1991 3
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however, the contribution of the protonated acid HA becomes larger than the dissociated form A- only if it interads strongly with micelles. This is the case for trichlorophenols. Therefore, for these compounds, P H A ~ H A> (PwA-po+ PA-pm). The interaction of the monochlorophenols is considerably less, to the extent that the solute mobility in the dissociated form is more than that in the HA form (Figure llc,d). In general, for less hydrophobic compounds, the difference between p m and PA-, is much larger than for the hydrophobic compounds. In other words, the changes in mobility with the pH variation are greater for the less hydrophobic monochlorophenols. The situation is different for the k’ vs pH function. The different in k’HAand kb,- increases with the solute hydrophobicity. The k b,- value is almost zero for all the solutes, indicating a small interaction of the anion with the micelles. On the other hand, the ktm values increase with the increase in solute hydrophobicity due to an increase in the partition coefficient into micelles. Figure 12 shows the variations of mobility and k‘ with pH for a mono- and a trichlorophenol. Note that the trend of the change in mobility is different for the various chlorophenols, while the change in retention factors with pH follows the same pattern for all the compounds. These two situations seem to contradict one another as far as the effect of pH on selectivity is concerned. Based on the mobility data, for more hydrophobic solutes, pH is not an effective parameter for selectivity manipulation since there is not much difference in the mobilities of the protonated and the dissociated forms of an acid. On the other hand, one would observe a drastic change in k’as the degree of the acid dissociation is changed through pH variations. Note, however, that the retention factor represents the degree of solute interactions with micelles. The degree of this interaction does not necessarily indicate the true migration behavior of ionizable solutes in MECC; therefore, mobility is probably a more representative parameter for solute migration. Work is presently underway to study the implication of this phenom-
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Flgum 13. Titratkn of 2CP (-), 25CP (---),245CP k), and pentaCP (- -) with 0.005 M NaOH in (a)aqueous and (b) 50 mM SDS solutions.
Ionic strength without SDS = 50 mM using NaCI. Horizontal lines represent the pK,. The equivalence polnt at - 5 mL of NaOH is from HCI used to acidify the sample. enon on optimization strategy for separation of ionic solutes in MECC. Micelle-Induced pK, Shift. One important factor that should be considered in a study of the pH effect on the migration behavior and separation of ionizable compounds by MECC is the micelle-induced pK, shift. Consideration of the micelle-induced shift of ionization constants is important in the comparison of the capabilities of MECC and CZE for the separation of ionizable compounds. The extent of ionization of acids in the MECC system depends on the apparent ionization constant in micellar solutions, which is different from the aqueous ionization Constants. More importantly, the magnitude of the pK, shift is a function of the solute’s structural properties. Equation 20 can be rewritten as ApK, = log (1+ ~ H A [ M ]-)log (1 + K”,-[M])
(28) Equations 20 and 28 show that the extent of the pK, shift is dependent on the difference in the binding constants of a weak acid and ita conjugate base to micelles. This would create two interesting situations. The first is when two compounds with very similar pK, values in aqueous solutions would have a very different pK, in micellar media. We have recently reported one such example for amino acids and small peptides and discussed the implications of this phenomenon on the selectivity in micellar liquid chromatography (29). In the presence of micelles, however, the different pK, shifts for various compounds translates into different net charges on the molecule at a given pH. The consequence of this phenomenon is an enhanced separation selectivity; in other words, larger variations in selectivity with pH can be observed in MECC compared to CZE. As a result, pH can be more effectively used to enhance the separation selectivity in MECC. Another possibility is that compounds with widely different pK, values in aqueous media and different lipophilicities would have similar ionization constants in micellar solution. Figure 13 illustrates the titration curves for four chlorophenols in purely
ANALYTICAL CHEMISTRY, VOL. 63, NO. 17, SEPTEMBER 1, 1991
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1829
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from individual experiments. Peak heights are arbitrary and vary to assist in peak identification.
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