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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma

Separation of very hydrophobic analytes by micellar electrokinetic chromatography IV. Modeling of the effective electrophoretic mobility from carbon number equivalents and octanol–water partition coefﬁcients夽 Carolin Huhn, Ute Pyell ∗ University of Marburg, Department of Chemistry, Hans-Meerwein-Strasse, D-35032 Marburg, Germany

a r t i c l e

i n f o

Article history: Received 18 February 2008 Received in revised form 22 April 2008 Accepted 25 April 2008 Available online 1 May 2008 Keywords: Carbon number equivalents Martin equation Modeling Octanol–water partition coefﬁcient Effective electrophoretic mobility

a b s t r a c t It is investigated whether those relationships derived within an optimization scheme developed previously to optimize separations in micellar electrokinetic chromatography can be used to model effective electrophoretic mobilities of analytes strongly differing in their properties (polarity and type of interaction with the pseudostationary phase). The modeling is based on two parameter sets: (i) carbon number equivalents or octanol–water partition coefﬁcients as analyte descriptors and (ii) four coefﬁcients describing properties of the separation electrolyte (based on retention data for a homologous series of alkyl phenyl ketones used as reference analytes). The applicability of the proposed model is validated comparing experimental and calculated effective electrophoretic mobilities. The results demonstrate that the model can effectively be used to predict effective electrophoretic mobilities of neutral analytes from the determined carbon number equivalents or from octanol–water partition coefﬁcients provided that the solvation parameters of the analytes of interest are similar to those of the reference analytes. © 2008 Elsevier B.V. All rights reserved.

1. Introduction In micellar electrokinetic chromatography (MEKC) the optimization of the composition of the separation electrolyte with regard to obtaining adequate resolution for the analytes of interest and/or minimizing the runtime has been mainly accomplished by one-parameter-optimization schemes varying the concentration of a single additive. Although a one-parameter-at-a-time variation approach can be successful [1–4], the global optimum is not necessarily reached. Computer-assisted schemes for the optimization of separation conditions regarding simultaneously several selected parameters should be preferred and different procedures of modeling retention data or separations (retention factors and/or migration times and/or electrophoretic mobilities) have been published, some were reviewed in [5,6]. Several multivariate chemometric designs were used to optimize the composition of a separation electrolyte within a deﬁned parameter space, e.g. regarding the concentration of the pseudostationary phase and the concentration of an organic modiﬁer as crucial parameters [7–12]. These procedures are based on experimentally determined depen-

夽 Presented at 4th Nordic Separation Science Society International Conference, Kaunas, Lithuania, August 2007. ∗ Corresponding author. Fax: +49 6421 2822124. E-mail address: [email protected] (U. Pyell). 0021-9673/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2008.04.061

dencies of retention data on variations of the separation conditions. Empirical (and theoretical) models for resolution optimization in MEKC were compared by van Zomeren et al. [13] and Garc´ıa-Ruiz et al. [14]. A new approach in this ﬁeld is the use of neuronal networks [15,16]. Also retention indices and octanol–water-partition coefﬁcients were used for the prediction of retention factors and the modeling of separations [17,18]. Other procedures are based on the solvation parameter model [19]. These procedures have been applied both in HPLC and in MEKC. In the solvation parameter model, ﬁve coefﬁcients (capital letters) and six descriptors (small letters) are used to characterize (for neutral compounds) the distribution between two condensed phases: the aqueous electrolyte and the pseudostationary phase. These coefﬁcients and descriptors represent the different types of interaction of the solute with the aqueous electrolyte and the pseudostationary phase. The retention factor k of a solute can then be described using log k = c + vV + eE + sS + aA + bB

(1)

with the analyte descriptors V, E, S, A, and B and the separation electrolyte coefﬁcients c, v, e, s, a and b. A detailed description of these parameters is given in [19]. Retention factors can be predicted if the separation electrolyte coefﬁcients and the analyte descriptors are known [20,21]. It should be noted, however, that the solvation parameter model has never been designed to predict retention

C. Huhn, U. Pyell / J. Chromatogr. A 1198–1199 (2008) 208–214

factors in order to optimize separations, its use is mainly in identifying the relative importance of the different types of intermolecular interactions between a solute and the two phases involved in the separation process. If the solvation parameter model is used for the prediction of retention factors, multiple linear regression is needed in combination with relatively large data sets for a statistically correct interpretation. The solvation parameter model can also be used to select a pseudostationary phase with high separation selectivity for the analytes of interest [19–23]. Another approach to model retention factors can be based on the octanol–water partition coefﬁcient POW . It was shown that there is a linear relationship between the retention index and POW and between log k and log POW [18,24]. With these data, retention factors but not migration times can be modeled. However, for many pseudostationary phases a congeneric behavior was observed for different types of solutes. For sodium dodecyl sulfate (SDS) as pseudostationary phase three analyte classes (i) hydrophobic solutes, (ii) polar hydrogen bond donating (HBD) solutes and (iii) polar hydrogen bond accepting solutes (HBA) can be distinguished, each having a different slope when plotting log k versus log POW . The same behavior was observed using retention indices instead of retention factors. Trone et al. [24] showed that this congeneric behavior can be attributed to stronger interactions via hydrogen bonding present with SDS as pseudostationary phase compared to the octanol–water system. There is also a model based on the principle of additivity of functional group contributions to the change in the free energy related to the transfer of a solute from the surrounding aqueous phase into the micellar pseudophase. This model was applied to benzene derivatives regarding the inﬂuence of functional groups attached to the benzene moiety [25]. In this paper we investigate the applicability of the previously proposed optimization scheme [17,26] to predict effective electrophoretic mobilities for selected analytes evoking different types of interaction with the pseudostationary phase. With the equations presented the effective electrophoretic mobility of a solute in a separation electrolyte characterized by four coefﬁcients can be calculated either from carbon number equivalents or from octanol–water partition coefﬁcients (provided that the solvation parameters of the analytes of interest are similar to those of the reference analytes). The reader is provided with a database of separation electrolyte coefﬁcients for 35 separation electrolytes containing SDS and varying concentrations of acetonitrile, urea and CaCl2 . This database is calculated from retention data for the homologous series of alkyl phenyl ketones used as reference analytes. The carbon number equivalents and effective electrophoretic mobilities of 18 model analytes were determined for selected compositions of the separation electrolyte. A comparison of experimental and modeled data is presented. 2. Materials and methods 2.1. Chemicals Methanol, anthracene, naphthaline, acridone were from Fluka, Buchs, Switzerland; urea and SDS from Roth, Karlsruhe, Germany; disodium tetraborate, CaCl2 , ethylvanillin, acetophenone, propiophenone, butyrophenone and valerophenone from Merck, Darmstadt, Germany; acetonitrile from J.T. Baker, Deventer, The Netherlands; pyrene, ﬂuorene, 3-nitrobenzene sulfonic acid, aniline, ethylaniline, propylaniline, butylaniline, pentylaniline, hexylaniline, hexanophenone, heptanophenone, octanophenone, decanophenone and dodecanophenone from Aldrich, St. Louis, MO, USA; caffeine from Sigma, Steinheim, Germany;

209

Table 1 Compositions of the separation electrolytes employed, c(Na2 B4 O7 ) = 1.875 mmol/L, c(SDS) = 60 mmol/L, pH 9.2. Additive

Buffer A

Buffer B

Buffer C

Buffer D

Acetonitrile Urea CaCl2

– – –

10% – –

– 4 mol/L –

20% 4 mol/L 0.5 mmol/L

2-nitrobenzaldehyde from Acros, Geel, Belgium; vanillin from ¨ Janssen, Bruggen, Germany; coumarin and 7-hydroxycoumarin were available at the Department of Chemistry, Marburg, Germany. Structures of the analytes selected are depicted in Fig. 1. 2.2. Buffer and sample preparation Analytes were dissolved in methanol at a concentration of 10 mmol/L. For injection, these standard solutions were diluted in a mixture of water and separation electrolyte (1:1) to a concentration appropriate for detection. All separation electrolytes contained 1.875 mmol/L Na2 B4 O7 and 60 mmol/L SDS, pH 9.2. Three buffer additives were used: acetonitrile, urea and CaCl2 . The concentrations of these additives in the different separation electrolytes tested are listed in Table 1. 2.3. Instruments A Beckman P/ACE 5510 equipped with a diode array detector (abs = 200 nm) was used. Sample injection was done at 34.5 mbar (0.5 psi) for 3 s. Fused silica capillaries from Polymicro Technologies (Phoenix, AZ, USA) were used with an inner diameter of 50 m and an outer diameter of 363 m. The length was set to 20/27 cm. New capillaries were conditioned by ﬂushing them ﬁrst with NaOH solution (0.1 mol/L) for 30 min and subsequently with run buffer for 10 min. A rinsing step with run buffer for 1 min was used for cleaning the capillary between runs. A voltage of 10 kV was applied for separation. After changing the composition of the separation electrolyte, a short rinsing step with 0.1 mol/L NaOH was used followed by rinsing with the new buffer. Origin 6.0 from Microcal Software, Northhampton, MA, USA was used for data analysis. The iteration procedure for the determination of the migration time of the micelles was programmed in Excel (Microsoft, Seattle, WA, USA). 3. Theoretical background 3.1. Separation electrolyte coefﬁcients In a previous paper [26] it was shown that four coefﬁcients calculated from the retention data of a homologous series can be used to characterize the properties of a separation electrolyte and to describe the inﬂuence of additives on the separation of neutral analytes. These four coefﬁcients are the mobility of the electroosmotic ﬂow (EOF) 0 , the effective electrophoretic mobility of the micelles eff,MC and the coefﬁcients a and b, intercept and slope of a regression line according to the Martin equation, when plotting log k versus the number of methylene units in the alkyl chain for members of a homologous series. The parameters a, b and the migration time of the micelles tMC (or eff,MC ) can simultaneously be obtained using the iteration procedure published by Bushey and Jorgenson [27,28]. With this procedure the separation electrolyte coefﬁcients have been obtained for different compositions of the separation electrolyte based on a borate buffer with 60 mmol/L SDS and varying concentrations of acetonitrile, urea and CaCl2 . An overview of the parameter range investigated is given in Tables 2–4.

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Fig. 1. Structures of the analytes.

Retention data were obtained for the separation of nine members of the homologous series of alkyl phenyl ketones. Each run was repeated three times. The migration times of all analytes being below 40 min and the migration time of the EOF marker (methanol) were included in the iteration procedure. The iteration was stopped after 30 steps. It has to be stressed, that in some cases the number of alkyl phenyl ketones employed for the calculation of separation electrolyte coefﬁcients was lower than 9 due to the following reasons: (i) the retention factors for the alkyl phenyl ketones in many separation electrolytes with low content of organic modiﬁers were so high that those members of the homologous series with high carbon number comigrated and effectively could be regarded as micelle marker. (ii) With the simultaneous addition of all three additives the restricted elution mode was reached and the migration times of the long alkyl chain homologues were too

Table 2 Separation electrolyte coefﬁcients a, b, eff,MC and 0 (mean values, n = 3) for separation electrolytes with curea = 0 mol/L and c(CaCl2 ) = 0 mmol/L (Type I) and with curea = 4 mol/L and c(CaCl2 ) = 0 mmol/L (Type II) ( A = volume concentration of ace-

tonitrile, electrophoretic mobilities given in 10−4 cm2 V−1 s−1 )

high to be determined within an acceptable time frame. It should be noted that the number of homologues included in the iteration procedure strongly inﬂuences the precision of the data obtained [29]. 3.2. Analyte descriptors 3.2.1. Carbon number equivalents In a previous paper [17], we introduced carbon number equivalents Nc∗ , which can be used as analyte descriptors, because they were shown to be quasi-independent of the composition of the separation electrolyte. Carbon number equivalents were deﬁned as the interpolated values using the Martin equation (Eq. (2)) from the plot of log k versus the number of methylene units in the alkyl chain of

Table 3 Separation electrolyte coefﬁcients a, b, eff,MC and 0 (mean values, n = 3) for separation electrolytes with A = 0% and c(CaCl2 ) = 0 mmol/L (Type III) and with A = 20% and c(CaCl2 ) = 0 mmol/L (Type IV) ( A = volume concentration of acetonitrile, electrophoretic mobilities given in 10−4 cm2 V−1 s−1 ) curea (mol/L)

A (%)

0 5 10 15 20 25

Type I

Type II

0

eff,MC

a

b

0

eff,MC

a

b

2.35 2.18 2.06 1.91 1.71 1.52

−1.49 −1.54 −1.55 −1.59 −1.55 −1.39

−0.05 −0.26 −0.48 −0.56 −0.65 −0.74

0.27 0.31 0.37 0.31 0.26 0.22

1.97 1.80 1.61 1.49 1.36 1.22

−1.52 −1.49 −1.37 −1.34 −1.27 −1.19

−0.34 −0.48 −0.71 −0.81 −0.94 −1.03

0.32 0.31 0.33 0.29 0.25 0.22

Data in part taken from Ref. [27].

0 1 2 3 4 5

Type III

Type IV

0

eff,MC

a

b

0

2.86 2.73 2.62 2.47 2.31 2.15

−1.69 −1.66 −1.70 −1.67 −1.63 −1.59

−0.15 −0.25 −0.32 −0.45 −0.58 −0.73

0.29 0.33 0.31 0.35 0.37 0.38

1.92 1.72 1.59 1.53 1.42 –a

Data in part taken from Ref. [27]. a Not determined.

eff,MC −1.55 −1.53 −1.43 −1.40 −1.29 –a

a −0.65 −0.72 −0.82 −0.87 −1.05 –a

b 0.26 0.24 0.24 0.23 0.24 –a

C. Huhn, U. Pyell / J. Chromatogr. A 1198–1199 (2008) 208–214 Table 4 Separation electrolyte coefﬁcients a, b, eff,MC and 0 (mean values, n = 3) for separation electrolytes with curea = 0 mol/L and A = 0 % (Type V) and with curea = 4 mol/L and A = 20 % (Type VI) ( A = volume concentration of acetonitrile, electrophoretic mobilities given in 10−4 cm2 V−1 s−1 ) c(CaCl2 ) (mmol/L)

Type V

0 0.25 0.5 0.75 1 1.5 2 2.5 5 7.5

Type VI

0

eff,MC

a

b

0

eff,MC

a

b

2.68 –a –a –a 2.58 –a –a 2.48 2.30 2.00

−1.62 –a –a –a −1.66 –a –a −1.69 −1.71 −1.76

−0.08 –a –a –a −0.09 –a –a −0.09 −0.13 −0.13

0.28 –a –a –a 0.27 –a –a 0.27 0.26 0.33

1.36 1.22 1.09 1.06 1.05 0.97 0.82 –a –a –a

−1.26 −1.25 −1.26 −1.29 −1.28 −1.37 −1.28 –a –a –a

−0.94 −0.94 −0.83 −0.91 −0.90 −0.89 −1.22 –a –a –a

0.26 0.25 0.24 0.25 0.26 0.26 0.32 –a –a –a

Data in part taken from Ref. [27]. a Not determined.

the members of a homologous series (here alkyl phenyl ketones) log k = a + b Nc∗

1 log b

Nc∗ =

1 log b

tR − t0 t0 (1 − tR /tMC )

Table 5 Carbon number equivalents Nc∗ determined from effective electrophoretic mobilities in Buffer C (see Table 1 predicted octanol–water partition coefﬁcients (log POW ) with associated standard deviation (SD) for values determined according to different methods [32], and carbon number equivalents Nc∗ (from log POW ) calculated from predicted log POW

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Naphthaline Anthracene Pyrene Fluorene Acridone 7-Hydroxycoumarin Coumarin 3-Nitrobenzene sulfonic acid Vanillin 3-Ethylvanillin 2-Nitrobenzaldehyde Caffeine Aniline 4-Ethylaniline 4-Propylaniline 4-Butylaniline 4-Pentylaniline 4-Hexylaniline

Nc∗

log POW

SD

Nc∗ (from log POW )

3.61 7.76 11.79 5.21 4.23 1.44 1.62 1.74 1.63 1.48 0.79 0.16 −0.66 1.62 2.85 4.09 5.28 6.35

3.27 4.26 4.57 3.99 2.66 1.35 1.70 −0.32 1.17 1.43 1.54 −0.21 1.15 2.09 2.57 3.07 3.58 4.08

0.12 0.52 1.16 0.29 0.69 0.39 0.31 0.89 0.26 0.18 0.21 0.33 0.25 0.21 0.19 0.18 0.19 0.23

4.07 6.04 6.66 5.50 2.85 0.24 0.94 −3.09 −0.12 0.40 0.62 −1.83 −0.16 1.72 2.67 3.67 4.68 5.68

(2)

Using Eq. (2), the carbon number equivalent Nc∗ of a neutral solute can be calculated directly from its experimental retention time tR or its effective electrophoretic mobility eff,R as described in Eqs. (3) and (4), by replacing k with the equation derived by Terabe et al. [30,31] Nc∗ =

211

eff,R eff,MC − eff,R

−a

(3)

−a

(4)

Employing Eq. (4), carbon number equivalents were determined for a number of selected analytes. The structures are depicted in Fig. 1. The selection includes hydrophobic aromatic hydrocarbons without further substituents (naphthaline, anthracene, pyrene and ﬂuorene) and more polar analytes with hydrogen bonding properties. The latter are acridone, caffeine, nitrobenzaldehyde, coumarin, and the homologous series of p-alkylanilines, which can accept hydrogen bonds due to the presence of keto and aromatic amino groups. In addition, analytes with hydrogen bond donating phenolic substituents were included (vanillin, ethylvanillin and hydroxycoumarin). For this class of analytes, however, a partial deprotonation has to be expected at pH 9.2. Nitrobenzene sulfonic acid was included as a fully dissociated ionic analyte. The carbon number equivalents determined with Buffer C (see Table 1) are listed in Table 5. Comparing the carbon number equivalents obtained with different separation electrolytes (data not shown), a high scattering of data was obtained for those analytes migrating close to t0 or tMC and having very high or low carbon number equivalents (aniline, caffeine, pyrene, hydroxycoumarin). This imprecision of data has already been reported for the prediction of retention factors [25,29]. However, this imprecision is not critical, because it does not result in a high imprecision concerning effective electrophoretic mobilities or migration times. For the very polar analytes high scatter is also due to the fact that the migration time is smaller than that of acetophenone, the member of the homologous series with the shortest alkyl chain. Very strong scatter in Nc∗ was also obtained for the solutes partially or fully ionized, as this approach is not valid in this case.

3.2.2. Octanol–water partition coefﬁcients In Table 5 the octanol–water partition coefﬁcients obtained via VCCLAB, Virtual Computational Chemistry Laboratory [32] are listed. From plotting the octanol–water partition coefﬁcients of the alkyl phenyl ketone homologues against their carbon numbers the following equation was obtained: log POW = c + dNc , with c = 1.229 and d = 0.502. This equation can be employed for the calculation of carbon number equivalents from their log POW values. The results of this procedure are given in Table 5 as Nc∗ (from log POW ). A graphical comparison of experimentally determined Nc∗ and those calculated from log POW is presented in Fig. 2. There is a high correlation between Nc∗ (from log POW ) and Nc∗ (exp) for the hydrogen bond acceptor analytes. An acceptable correlation is given for some of the aromatic hydrocarbons (marked with a square in Fig. 2), except the most hydrophobic analyte pyrene, which migrates close to tMC

Fig. 2. Comparison of carbon number equivalents Nc∗ (exp) calculated from experimental data for Buffer C and carbon number equivalents Nc∗ (from log POW ) determined from octanol–water partition coefﬁcients (see Table 5), solid line = regression line. Aromatic hydrocarbons are marked with a square, partially or fully ionized analytes are marked with a circle, numbering according to Fig. 1.

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Table 6 Mean value x¯ , standard deviation SD and relative standard deviation RSD (in %) of the coefﬁcients a, b, 0 , eff,MC calculated from 6 (Buffer A) or 4 (Buffers B–D) measurements at different days in different capillaries /(10−4

cm2

V−1 s−1 )

a

b

0

eff,MC

x¯ SD RSD

−0.095 0.039 40.420

0.301 0.032 10.544

2.492 0.09 6.81

−1.53 0.03 1.86

x¯ SD RSD

−0.489 0.006 −1.173

0.356 0.010 2.698

2.089 0.045 2.927

−1.523 0.016 1.075

x¯ SD RSD

−0.556 0.056 10.06

0.387 0.013 3.316

2.201 0.047 3.191

−1.592 0.023 1.452

x¯ SD RSD

−0.926 0.010 1.091

0.252 0.003 1.380

1.281 0.145 5.715

−1.396 0.027 1.959

/(10−4

cm2

V−1 s−1 )

A

B

C

D

in Buffer C. A large mismatch is obvious for the fully dissociated sulfonic acid. The partially ionized analytes (marked with circles) also show relatively large deviations for Nc∗ (from log POW ) from Nc∗ (exp). Not taking into account the ionic analytes (for which the method is not appropriate) and pyrene, a linear regression yields Nc∗ (exp) = 0.56 + 0.98 Nc∗ (from log POW ) with a correlation coefﬁcient of R = 0.948. Including the partially ionized analytes, but not nitrobenzene sulfonic acid in the regression analysis we obtain Nc∗ (exp) = 0.84 + 0.92 Nc∗ (from log POW ) with a correlation coefﬁcient of R = 0.944. Values strongly deviating from the expected line (intercept = 0, slope = 1) are obtained when nitrobenzenesulfonic acid is included (intercept = 1.39, slope = 0.75 and R = 0.881). 4. Modeling of the effective electrophoretic mobility In order to investigate the precision of the parameters a, b, 0 and eff,MC these data were determined several times with four different compositions of the separation electrolyte (Table 6). Measurements were recorded on different days and in different capillaries. Table 6 shows that for 0 there is a high RSD as expected for this parameter. Noticeable is the elevated RSD for a and b for Buffer A. This elevated RSD is due to the low number of members of the homologous reference series which can be included in the iteration procedure. In general, deviation is expected to be mainly due to non-thermostated measurement conditions and to changes in the inner capillary surface properties inducing drifting phenomena. The viability of the proposed approach was investigated by the calculation of effective electrophoretic mobilities for the analytes depicted in Fig. 1 from the data listed in Table 5 for Nc∗ and Nc∗ (from log POW ) and from the parameters listed in Tables 2–4 employing Eq. (4). Linear regression lines in the form eff (mod) = t + meff (exp) are obtained. The prediction ability of the model was tested by calculation of the slope, the intercept and the correlation coefﬁcient of the regression line. Ideally there is no signiﬁcant deviation of the slope from 1 and the intercept from 0. Alternatively, a paired t-test was employed with the same set of data. Tabulated t-values were taken from [33]. 4.1. Carbon number equivalents The calculation of tR or eff,R is possible, if Nc∗ of an analyte and the parameters a, b, 0 and eff,MC of the separation electrolyte are

known: ∗

eff,R =

eff,MC 10a+bNc a+bNc∗

1 + 10

(5)

The parameter eff,R (for Buffers A, B and D) was calculated for the selected model analytes from carbon number equivalents determined with Buffer C (see Tables 1 and 5) and the separation electrolyte coefﬁcients listed in Tables 2–4. In Fig. 3 the calculated values are compared to the experimentally determined data. The same calculation was additionally carried out using the parameters given in Table 6 instead of the parameters in Tables 2–4. There is no signiﬁcant difference (paired t-test, ˛ = 0.05) between effective electrophoretic mobilities calculated with both data sets for the separation electrolytes B and D. However, a signiﬁcant difference is observed for Buffer A which can be attributed to the imprecision of the separation electrolyte coefﬁcients discussed in the previous section. In Fig. 3 four calculated data points (marked with a circle) show strong deviations from the experimental values. These data points were calculated for Buffer D containing CaCl2 as additive. The corresponding analytes hydroxycoumarin, vanillin, ethylvanillin and nitrobenzene sulfonic acid all carry a negative effective charge at pH 9.2. Possibly, there is ion pair formation between the ionic analytes and the divalent metal ion Ca2+ . A linear regression of the data in Fig. 3 (n = 54) leaving out the ionic analytes in separation electrolyte D, yields eff,cal = −0.038 + 0.945eff,exp with a correlation coefﬁcient R = 0.980. A t-test (signiﬁcance level of ˛ = 0.05) reveals that neither slope nor intercept are signiﬁcantly different from 1 or 0, respectively. In addition to the evaluation via a regression line, a paired t-test was performed with the same data, revealing that the calculated data are not signiﬁcantly different from the experimentally determined values at a signiﬁcance level of ˛ = 0.05. The modeling of effective electrophoretic mobilities was also done from the carbon number equivalents determined for the other three separation electrolytes (data not shown). The regression lines have slopes higher than 0.9 and intercepts smaller than 0.15. The

Fig. 3. Comparison of the effective electrophoretic mobility eff,cal modeled from data listed in Tables 2–5 using Eq. (5) and the experimentally determined electrophoretic mobility eff,exp for Buffers A, B and D; solid line = ideal line (slope = 1, intercept = 0), dashed dotted line = linear regression line, dotted line = conﬁdence interval (˛ = 0.05); data obtained for ionic analytes in Buffer D are marked with an ellipse and are not included in the regression analysis; for further experimental details refer to Table 1.

C. Huhn, U. Pyell / J. Chromatogr. A 1198–1199 (2008) 208–214

213

correlation coefﬁcients (plotting modeled data against experimentally determined data) are higher than 0.98 (excluding the data marked in Fig. 3). However, slopes of ca. 0.7 and intercepts of ca. −0.3 were obtained for those data calculated with carbon number equivalents determined for Buffer A, but still with high correlation coefﬁcient. 4.2. Octanol–water partition coefﬁcients When replacing Nc∗ with the term (log POW –c)/d (see Section 3.2.2) Eq. (6) is obtained. This equation makes it possible to model effective electrophoretic mobilities directly from tabulated octanol–water partition coefﬁcients provided that the separation electrolyte coefﬁcients a, b, and eff,MC are known eff,R =

eff,MC × 10a+b(log POW −c)/d 1 + 10a+b(log POW −c)/d

(6)

with c and d = regression line coefﬁcients. The homologous series of alkylanilines belongs to the same class of analytes as the reference series of alkyl phenyl ketones. For the alkylanilines, effective electrophoretic mobilities were calculated using Eq. (6) from log POW values (Table 5) and the separation electrolyte coefﬁcients listed in Tables 2–4. Fig. 4 shows the comparison of eff,cal and eff,exp for all four compositions of the separation electrolyte included in this study (see Table 1). The regression line including all data points corresponds to eff,cal = −0.040 + 0.938eff,exp with a correlation coefﬁcient R = 0.985. There is no signiﬁcant deviation (t-test, significance level of ˛ = 0.05) of the slope from 1 and the intercept from 0. A paired t-test (signiﬁcance level of ˛ = 0.05) with the data of Fig. 4 (including all data points, n = 24) reveals also that there is no signiﬁcant difference between the calculated and the experimentally determined data. Also the effective electrophoretic mobilities of the other analytes were calculated from log POW as described for the alkylanilines. The results for all analytes plotting eff,cal against eff,exp are shown in Fig. 5 for Buffer B (10% acetonitrile). The results for Buffers A, C and D are similar (data not

Fig. 5. Comparison of eff,cal (modeled via log POW and tabulated coefﬁcients a, b, eff,MC (Tables 2–4) employing Eq. (6) to eff,exp for all analytes (Fig. 1), Buffer B; (0) aniline, (2) ethylaniline, (3) propylaniline, (4) butylaniline, (5) pentylaniline, (6) hexylaniline; () hydrogen bond accepting solute, () non-hydrogen bonding solute, () hydrogen bond donating solute; solid line = ideal line (slope = 1, intercept = 0), dotted line = regression line for hydrogen acceptor solutes, dashed line = regression line for aromatic hydrocarbons.

shown). The different classes of compounds have to be evaluated separately: the results of those analytes having a negative effective electrophoretic mobility at pH 9.2 (open circles) do not show any correlation with eff,exp . The results for the hydrogen bond accepting solutes show a good correlation of calculated with experimental data. The linear regression for this class of analytes (for the data set obtained for Buffer B) yields eff,cal = 0.032 + 1.024eff,exp , with a correlation coefﬁcient of R = 0.972. However, the correlation is signiﬁcantly weaker compared to the results in Section 4.1, where the modeling was done using experimentally determined Nc∗ values (Table 5). In this case, for the same set of analytes a linear regression line of eff,cal = 0.010 + 1.040eff,exp , with a correlation coefﬁcient of R = 0.996 was obtained. Data obtained for the class of non-hydrogen bonding solutes, the aromatic hydrocarbons, were evaluated separately. The regression line plotting eff,cal against eff,exp shows a high correlation coefﬁcient of 0.996. As expected from the solvation parameter model, this regression line has slope and intercept differing signiﬁcantly from that obtained for the hydrogen bond accepting solutes (eff,cal = −0.637 + 0.637eff,exp ). If for this class of analytes effective electrophoretic mobilities are to be modeled from octanol–water partition coefﬁcients, a correction factor has to be introduced or a more suitable homologous series, e.g. alkylbenzenes has to be taken as reference. Acknowledgement C.H. thanks for ﬁnancial support from the Hessian Ministry of Science and Art. References

Fig. 4. Comparison of eff,cal (modeled via log POW and tabulated coefﬁcients a, b, eff,MC (Tables 2–4) employing Eq. (6) to eff,exp for all buffers (Table 1) and the alkylanilines (Fig. 1), solid line = ideal line (slope = 1, intercept = 0), dashed dotted line = linear regression line, dotted line = conﬁdence interval (˛ = 0.05); for further experimental details refer to Table 1.

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