Multicomponent (n ≥ 3) Sorption Isotherms in Reversed-Phase Liquid

Mar 22, 2010 - Comparison of concentration pulse and tracer pulse chromatography: Experimental determination of eluent uptake by bridged-ethylene hybr...
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Anal. Chem. 2010, 82, 3329–3336

Multicomponent (n g 3) Sorption Isotherms in Reversed-Phase Liquid Chromatography: The Effect of Immobilized Eluent on the Retention of Analytes Jennifer Mallette, Mei Wang, and Jon F. Parcher* Chemistry Department, University of Mississippi, University, Mississippi 38677 The experimental technique of tracer pulse chromatography was used to simultaneously measure the uptake of eluent components by a C18-bonded reversed-phase liquid chromatography (RPLC) packing and the retention factors for a series of test analytes over the full range of eluent composition for methanol and acetonitrile with water. The primary objective of the research was to determine whether or not the uptake of eluent components immobilized as part of the stationary phase would influence the retention of analyte standards. Both acetonitrile and methanol were absorbed in or adsorbed on the C18-bonded phase with the maximum amount of acetonitrile sorbed being about four times that of methanol. The thermodynamic void volume of the column and the excess sorption isotherms of acetonitrile, methanol, and water in binary aqueous/organic mixtures were determined directly from the tracer pulse experiments. The absolute sorption isotherms of the eluent components were indirectly estimated by a combination of techniques. Regression analysis of the nonstationary inflection point of the excess isotherms provided an estimate of the volume of eluent sorbed by the stationary phase but only over a limited eluent composition range. In order to expand the applicable composition range, several commonly used “unretained” probe solutes were tested to determine the accuracy of the assumption that the retention volumes of these solutes provided a viable measure of the kinetic void volume (mobile-phase volume) of the column. The difference between the thermodynamic and kinetic void volumes provided an estimate of the absolute volume of eluent present in the stationary phase. The experimental results showed that some solutes, viz., water and thiourea, did provide an accurate measure of the mobile-phase volume but only over a limited range of eluent composition. Using deuterated water as the unretained dead time marker for water-rich eluents combined with the regression results from excess isotherm data, the absolute volume of eluent sorbed by the stationary phase could be estimated over the full range of eluent composition. The effect of this 10.1021/ac100148b  2010 American Chemical Society Published on Web 03/22/2010

uptake of eluent on the retention of the test solutes appeared to be minimal for this particular set of test analytes. It has long been recognized that a clear relationship exists between the shape and temporal distribution of an analyte elution profile and the equilibrium isotherm of the analyte between the stationary and mobile phases for all types of chromatography. This thermodynamic basis for chromatography is particularly important for preparative scale procedures where the column is often overloaded and the isotherms and peak shapes can be somewhat bizarre. In analytical chromatography, distribution isotherms are particularly crucial for our understanding of the multifaceted retention mechanisms observed in reversed-phase liquid chromatography (RPLC). The multiplicity of retention mechanisms arises from the complex nature of the interfacial region between the stationary and mobile phases and the unique properties of hydrocarbon “liquids” chemically bonded to solid silica. The complexity of RPLC systems has been discussed extensively along with the apparent heterogeneity of the stationary phase in bonded packing systems with aqueous-organic eluents.1-3 In order to determine the influence of thermodynamic equilibria in such complex systems, it is sometimes necessary to concurrently measure the competitive isotherms of several components in a RPLC system. These components often include eluents as well as analytes; because with bonded-phase packings, the organic, and sometimes even the aqueous, component of the eluent can interact with the bonded moiety to become part of the stationary phase at least on a short time scale. Because of experimental difficulties, analyte distribution isotherms are usually determined with an arbitrary but fixed eluent composition,4,5 and the volume of mobile phase is usually determined from the retention volume of a purportedly unretained solute. On the other hand, the distribution isotherms of eluent components are usually determined over a wide composition range without regard to analytes. To complicate matters further, the eluent isotherms are * To whom correspondence should be addressed. E-mail: [email protected]. (1) Gritti, F.; Guiochon, G. J. Chromatogr., A 2005, 1099, 1–42. (2) Kazakevich, Y. V.; LoBrutto, R.; Chan, F.; Patel, T. J. Chromatogr., A 2001, 913, 75–87. (3) Gritti, F.; Guiochon, G. Anal. Chem. 2006, 78, 5823–5834. (4) Gritti, F.; Guiochon, G. Anal. Chem. 2006, 78, 4642–4653. (5) Felinger, A.; Cavazzini, A.; Guiochon, G. J. Chromatogr., A 2003, 986, 207– 225.

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most often described in terms of excess quantities, whereas the solute isotherms are usually expressed as absolute amounts of a solute contained in or on the stationary phase. In a recent study of the effect of organic modifiers, Gritti and Guiochon6 used two different chromatographic methods to determine the absolute adsorption isotherms of phenol and caffeine solutes and the excess adsorption of acetonitrile used as an eluent component. The solute isotherms were measured by M frontal chromatography over a concentration range of 0 e θSolute e 0.05-0.10 using thiourea as the dead time marker probe. The excess isotherm of the eluent was measured with concentration pulse chromatography over the full composition range. The thermodynamic void volume was determined by integration of the concentration pulse retention data also over the full eluent composition range. The literature describing studies of distribution isotherms for multiple components (n g 3) in RPLC systems is somewhat sparse due to the complexity and difficulty of the experimental procedures available for the investigation of RPLC systems in situ. The earliest investigation of the uptake of eluent components by a bonded stationary phase with ternary eluent systems was carried out with eluents composed of acetonitrile, carbon tetrachloride, and water.7 The experimental technique was tracer pulse chromatography with radioactive isotopes. The excess volumes of each eluent component in the stationary phase were determined at numerous binary and five ternary compositions. More recently, the same type of investigations were carried out with binary and ternary eluents composed of acetonitrile, methanol, and water.8 The experimental technique was tracer pulse chromatography with stable isotopes and a mass specific detection system.9 The excess volumes of the eluents in a C18bonded stationary phase were measured for 30 binary and 16 ternary eluents. In addition to the study of the uptake of eluent components, sorption isotherms of multiple analytes in systems with a fixed eluent composition have also been investigated. In 2000 and 2001, two very similar studies were published10,11 involving the use of full cycle frontal analysis chromatography to simultaneously determine the sorption isotherms of three phenyl alcohols in RPLC systems. The eluents were 1:1 mixtures of methanol and water. In these studies, the absolute amount of analyte (not the excess) taken up by the stationary phase was measured using either thiourea10 or solvent peaks11 as a measure of the volume of mobile phase in the column. Multicomponent equilibria of racemic mixtures of enantiomeric analytes with the stationary phase have been investigated using bonded, chiral stationary phases. The peak perturbation chromatographic method was used to measure the competitive sorption isotherms of methyl and ethyl mandelate enantiomers.12 The eluent used in this investigation was 1.4% methanol in water Gritti, F.; Guiochon, G. Anal. Chem. 2005, 77, 4257–4272. Knox, J. H.; Kaliszan, R. J. Chromatogr. 1985, 349, 211–234. Wang, M.; Mallette, J.; Parcher, J. Anal. Chem. 2009, 81, 984–990. Wang, M.; Mallette, J.; Parcher, J. F. Anal. Chem. 2008, 80, 6708–6714. Quinones, I.; Ford, J. C.; Guiochon, G. Chem. Eng. Sci. 2000, 55, 909– 929. (11) Lisec, O.; Hugo, P.; Seidel-Morgenstern, A. J. Chromatogr., A 2001, 908, 19–34. (12) Lindholm, J.; Forssen, P.; Fornstedt, T. Anal. Chem. 2004, 76, 5472–5478. (13) Arnell, R.; Forssen, P.; Fornstedt, T.; Sardella, R. J. Chromatogr., A 2009, 1216, 3480–3487. (6) (7) (8) (9) (10)

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buffered at pH 6. The enantiomers were studied in a quaternary mixture with a composition of 1:1:1:1. The mobile-phase volume was determined from the retention time of the “first buffer/water disturbance”. The measured isotherms were modeled with a biLangmuir equation with twelve adjustable parameters determined for the four solutes. More recently, the same group13 used a different chromatographic technique, elution-by-characteristic-point, to measure the sorption isotherms of the R and S forms of allyglycine as well as acetic acid on or in a chiral stationary phase. The eluent was a mixture of methanol/acetic acid and ammonium acetate (4:1) with the acetic acid acting as an additive to influence the peak shape of the enantiomeric analytes. This study was unique because the sorption isotherm of acetic acid was determined from the effect of this invisible additive on the retention of the analytes. The mobilephase volume was determined from the retention time of acetone in this study. The inverse method was used to determine the ten adjustable parameters required to describe the uptake of the two analytes and the modifier by the stationary phase.13 Recently, Asnin et al.14 measured the adsorption isotherms of the enantiomers of Naproxen as well as the eluent components water and methanol on a chiral stationary phase. The concentration pulse method was used for the eluent isotherms and an ancient but valid method proposed by Glueckauf15 was used to determine the absolute isotherm of Naproxen. In this case, the authors used the thermodynamic void volume in place of the kinetic void volume. The absolute isotherms of water and methanol were determined from excess adsorption data by assuming that the volume of eluent adsorbed was independent of the eluent composition. This led to the supposition that the concentration of water in this layer increased as the concentration of water in the bulk eluent increased. One general observation to be drawn from these studies is the idea that RPLC eluent components commonly interact with bonded stationary phases and the composition of the eluent acting as part of the stationary phase may significantly differ from the composition of the bulk eluent comprising the mobile phase. Thus, the actual stationary phase may consist of immobilized eluent components as well as the bonded phase of the packing material and the accessible silanol sites on the surface of the solid silica base material. The sorption isotherms of analytes over small concentration ranges can be used to predict the retention time and peak shape of the analytes as a function of analyte concentration at fixed eluent composition. However, there is still no clear correlation or model to quantitatively predict the effect of the uptake of eluent components on the retention and resolution of analytical solutes. This phenomenon could prove to be very important in gradient elution methods where the composition of the eluent varies with time. The purpose of the present investigation was to experimentally measure the uptake of eluent components from a binary mixture and the Henry’s law constants or retention factors of a series of test solutes at infinite dilution in the same experiment using tracer pulse chromatography. This data set could then serve as a basis for investigating the possible effect of eluent uptake on the retention of infinite dilution analytes. (14) Asnin, L.; Gritti, F.; Kaczmarski, K.; Guiochon, G. J. Chromatogr., A 2010, 1217, 264–275. (15) Glueckauf, E. J. Chem. Soc. 1947, 1302. (16) Everett, D. H. Pure Appl. Chem. 1986, 58, 967–984.

THEORY Excess and Absolute Volume of a Component in the Stationary Phase. The rationale for the use of excess quantities to describe the sorption of eluent components while using absolute quantities to describe the uptake of analytes centers on the difficulty of determining the volume, VM, of eluent that constitutes the mobile phase. This problem involves the specification of the exact position of the hypothetical Gibbs Dividing Surface which delineates the boundary between the adsorbed and bulk liquid phases.16 The volume of eluent in the mobile phase must be known in order to accurately measure the absolute amount of analyte or eluent in the stationary phase. The relation between the breakthrough volume of a frontal analysis front or the retention volume of an isotopically labeled solute, V*R,i, and the absolute amount or volume, ViS, of that component resident in the stationary phase is ViS)(V*R,i - VM)θiM

(1)

where θiMrepresents the volume fraction of unlabeled, organic component i in the bulk eluent constituting the mobile phase. This equation does not provide a viable method for the accurate determination of ViS without a precise value of the kinetic void volume,VM, and the literature is replete with discussions concerning the difficulties involved in the accurate determination of VM.7,17-19 Knox addressed this issue in the early literature by proposing definitions for two distinct types of void volume.7 The volume of the mobile phase was defined as the kinetic void volume while the total volume of eluent in the column was designated as the thermodynamic void volume. At the time, Knox expressed the opinion that an unambiguous definition of the mobile and stationary phase in RPLC was impossible.7 Although the determination of the kinetic void volume, VM, is problematic, the thermodynamic void volume, V0, is easily experimentally accessible from the relation: V0 )

∑ V* θ

M R,i i

(2)

If the thermodynamic void volume is substituted into eq 1, the result is an excess quantity. ViXS)(V*R,i - V0)θiM

(3)

The excess volume of component i in the stationary phase, ViXS, is defined using the /vNA convention as20

i in the system in excess of the volume of i that would be present in the same system with a totally inert adsorbent. The difference between the two measures of adsorption is given by the relation ViS - ViXS ) θiMVS. At low concentration of organic eluent, the difference between the excess and absolute volumes of this component adsorbed is minimal. Thus, it has been suggested that, at low solute concentration, there is no need to distinguish between the two types of adsorption or void volumes.14 The question of whether to experimentally measure the kinetic or thermodynamic void volumes, VMor V0, i.e., whether to report ViSor ViXSdata, has been an issue among chromatographers for decades. The question is sometimes decided by the degree of error that can be tolerated in the reported data. However, another important factor is the range of eluent compositions to be considered. With an eluent of fixed composition, it is sometimes possible to identify a dead time marker (solute) that does not strongly interact with the stationary phase at the particular eluent composition. This is often the case with solute isotherm measurements. However, no such solute has been identified that is unretained by the stationary phase over the full range of eluent composition commonly used for the determination of the sorption isotherms of eluent compositions. Retention Factors Calculated Using the Thermodynamic and Kinetic Void Volumes. The commonly used retention factor, ki(VM), gives a measure of the ratio of the amount or volume of a component present in the stationary and mobile phases when the chromatographic systems is at equilibrium. ki(VM) )

VR,i - VM

≡

ViS

-

VSθiM

) Vi -

V0θiM

(4)

where VS and Vi represent the total volume of eluent in the stationary phase and the total volume of component i in the system, respectively. ViXS represents the volume of component (17) Rimmer, C. A.; Simmons, C. R.; Dorsey, J. G. J. Chromatogr., A 2002, 965, 219–232. (18) Gritti, F.; Kazakevich, Y. V.; Guiochon, G. J. Chromatogr., A 2007, 1161, 157–169. (19) Kazakevich, Y. V.; McNair, H. M. J. Chromatogr. Sci. 1993, 31, 317–312. (20) Riedo, F.; Kovats, E. J. Chromatogr. 1982, 239, 1–28.

ViS ViM

(5)

VR,i represents the retention volume of component i in the system. In RPLC systems, accurate determination of VMover a range of eluent composition is problematic. The usual method to overcome this problem is to use the thermodynamic void volume, V0, instead of the kinetic void volume in the determination of the retention factor from retention volume data. ki(V0) )

VR,i - V0 V0

(6)

Unfortunately, this simple substitution minimizes the physical meaning of the retention factor. From eqs 3 and 4, the retention factor calculated from V0can be expressed as ki(V0) )

ViXS

VM

)

ViXS Vi - ViXS

(7)

In this case, the physical meaning of the retention factor is uncertain, and there is no clear relationship between ki(V0) and the equilibrium distribution of component i between the stationary and mobile phases. The retention factor, ki(V0), is experimentally accessible but is of questionable value for the elucidation of retention mechanisms. Model for the Role of the Stationary Phase in the Retention of Analytical Solute. Kazakevich et al.2 have proposed a model for the adsorption of eluent components on the surface of Analytical Chemistry, Vol. 82, No. 8, April 15, 2010

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Figure 1. Schematic diagram of the RPLC model proposed by Kazakevich et al.2

bonded packings in RPLC. This model posits that the eluent adsorbs on the surface of the bonded material as a separate phase which acts as a stationary phase itself. The only difference between the bulk eluent comprising the mobile phase and the adsorbed eluent layer on the bonded stationary phase is composition. The adsorbed layer is usually richer in the organic eluent component than the bulk mobile phase except for organic-rich eluent composition from which water may be selectively adsorbed. This model has been extended to include the adsorption of analytes by Gritti and Guiochon6 in a study of the effects of organic modifiers in RPLC. In this model, two Gibbs Dividing Surfaces would exist between (a) the adsorbed and bulk eluent and (b) between the analyte adsorbed at the surface of the bonded liquid and the analyte dissolved in the adsorbed eluent. Figure 1 illustrates this complex model for a strongly adsorbed eluent such as acetonitrile or tetrahydrofuran. For an eluent like methanol that only forms a monolayer of adsorbed eluent, the two Gibbs Dividing Surfaces would coincide.6 One possible consequence of this proposed model would be that the retention of analytical solutes should increase with the amount of organic eluent adsorbed on the stationary (bonded) phase assuming that the solutes are more soluble in the adsorbed eluent than in the nonpolar bonded phase. EXPERIMENTAL SECTION Chemicals. The HPLC grade eluents methanol, acetonitrile, and water, and the optima grade tetrahydrofuran were purchased from Fisher Scientific. Isotopic samples of methanol (methanold3, 99.8 atom % D), acetonitrile (acetonitrile-d3, 99.8 atom % D), acetone (acetone-d6, 99.5 atom % D), and water (water-d2, 99.8 atom % D) were obtained from Aldrich. Thiourea (>99.0%) was purchased from Sigma Aldrich. Column. The HPLC column used in this work was an Agilent ZORBAX Eclipse Plus C18 column. The column dimensions were 4.6 mm × 250 mm. The ZORBAX Rx-SIL support has a nominal surface area of 160 m2/g and a controlled pore size of 95 Å. The particle size was 5 µm. The bonding density was proprietary; however, the reported carbon loading was 9%. The thermodynamic void volume of the column was obtained by 3332

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Figure 2. Excess sorption isotherm of acetonitrile (b) and methanol (O) with a C18-bonded stationary phase. The lines represent the regression results for the data in the range 0.5 e θM i e 0.8 (acetonitrile) and 0.4 e θiM e 0.8 (methanol).

measuring the retention volumes of methanol-d3 or ACN-d3 and D2O over the composition range from 0% to 100% at a flow rate of 0.5 mL/min. Instrumentation. HPLC. The liquid chromatography system was a Hewlett-Packard 1050. This instrument included a single pump with a proportioning valve, an autosampler with a 25 µL sample loop, and ChemStation software. The extra column volume was 0.157 mL measured from the retention time of D2O without the column in the system. All the retention data reported in this work were corrected for this contribution. MS. The mass spectrometer was the detector in an Agilent 6120 Single Quad LC/MS instrument. This system included a multimode ionization source and a single quadrupole mass analyzer. The ionization source was capable of either atmospheric pressure electro-spray ionization (APESI) or atmospheric pressure chemical ionization (APCI). Experimental Procedures. HPLC Procedure. The experiments were carried out over the full range of eluent compositions from 0 to 100%. All the eluents were degassed prior to use. The column temperature was controlled at 25 °C (±0.1 °C). A 3 µL sample was injected and triple injections were made for each composition. MS Procedure. The mixture of tracers and analyte samples were detected in positive APCI mode. A manual tune was performed to established the optimum octopole and fragmentor voltages for the low mass isotope tracers (m/z < 50).The instrument was operated in a selected ion monitor (SIM) mode at characteristic m/z values for the labeled isotopes of each eluent component and the analyte samples. M + 1 ions were monitored for methanol-d3 (m/z 36), acetonitrile-d3 (m/z 45), acetone-d6 (m/z 65), tetrahydrofuran (m/z 73), and thiourea (m/z 77), respectively, except m/z 19 was monitored for D2O. The effect of isotopic labeling on the retention times of the probe solutes was investigated by measuring the relative retention times of labeled and natural probe solutes (acetonitrile, methanol, and water) in a column with a mobile phase that did not contain the probe component. The isotope effect was negligible in each case.

Table 1. Absolute Volumes of the Organic Eluent Component in the Stationary Phase Calculated from the Linear Region of the Excess Volume Isotherms

organic eluent acetonitrile methanol

total volume of eluent, VS, in the stationary phase (µL)

volume of organic eluent in the stationary phase, ViS(µL)

volume fraction of organic component in the stationary phase

455(±20) 94(±8)

408(±20) 78(±5)

0.90 0.83

RESULTS AND DISCUSSION Excess Isotherms of Eluent Components. The retention volumes of three isotopically labeled eluent components and six test solutes are given in Tables S-1 and S-2 (Supporting Information). The thermodynamic void volume of the column was determined from the isotopically labeled samples of acetonitrile, methanol, and water from eq 2. The excess volumes of acetonitrile and methanol with water were determined as a function of composition over the full eluent composition range from eq 3. The results are shown in Figure 2. Both organic eluents were selectively sorbed by the C18-bonded packing; however, acetonitrile was taken up by the stationary phase approximately four times as much as methanol. Absolute Isotherms of the Eluent Components. While it is relatively easy to measure the excess volume of eluent taken up by the stationary phase in a column, it is the absolute amount of eluent interacting with the stationary phase that is needed to evaluate any proposed retention model such as the one discussed in the Theory section. A data analysis technique proposed by Schay21 provides a method to estimate the absolute volume of the organic eluent component in the stationary phase as well as the total volume of eluent in the stationary phase and, thus, the volume fraction of the organic component in the eluent that constitutes a part of the stationary phase. The straight lines in

Figure 3. Absolute sorption isotherms for acetonitrile and methanol with a C18-bonded stationary phase. (O) Calculations assuming that water does not interact with the stationary phase in the range 0 e θiM e 0.4 (acetonitrile) and 0 e θiM e 0.3 (methanol). (0) Calculations assuming that VSi is constant in the range 0.5 e θM i e 0.8(acetonitrile) and 0.4 e θiM e 0.8(methanol). (∆) Calculations assuming that VS is constant in the range 0.5 e θiM e 1(acetonitrile) and 0.4 e θiM e 1(methanol). (b) Calculations assuming that VS is constant in the range 0 e θiM e 1.

Figure 2 show the regression results from the fit of eq 4 to the data in the range of 0.4 or 0.5e θiM e 0.8. The results from this regression scheme are presented in Table 1. The reported surface area of the packing in the column was 160 m2/g. Assuming that the acetonitrile is adsorbed as a separate phase on the surface of the C18-packing and the weight of the packing in the column was 2 g, the 408 µL volume of adsorbed acetonitrile would correspond to a film thickness of ca. 13 Å. The layer thickness for methanol would be approximately 3 Å. These values are in excellent agreement with those previously observed by Kazakevich,2,22 viz., 14 Å for acetonitrile and 2.5 Å for methanol. Unfortunately, however, this data analysis scheme only provides estimates of the volume of eluent in the stationary phase for the range of composition of 0.4 or 0.5e θiM e 0.8. In order to determine the absolute amount of eluent taken up by the stationary phase in the water-rich eluent composition range, it is necessary to postulate some ancillary condition. The two most common approaches assume that either the volume of eluent in

Figure 4. Calculated volume of acetonitrile (A) and methanol (B) in or on the stationary phase using the retention volume of three probe solutes as a measure of the mobile phase volume, VM: (0) deuterated water, (9) thiourea, (2) acetone. Analytical Chemistry, Vol. 82, No. 8, April 15, 2010

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mobile phase. The results for these two assumptions and the linear regression results are shown in Figure 3. There was about a 15-25% difference for the calculated values of the volume of acetonitrile in the stationary phase. However, the major difference between the two assumptions concerns the role of water. With the assumption that the volume of eluent in the stationary phase remains constant, the amount of water in that volume must increase as the amount of acetonitrile decreases.14 This is in direct conflict with the second assumption that water is not taken up by the stationary phase. The second assumption is the most reasonable in view of the hydrophobic nature of the bonded packing. However, this model requires that the total volume of eluent in the stationary phase must decrease to zero as θiM f 0. In summary, the best scheme for estimating absolute sorption isotherms from excess sorption data involves the use of different assumptions for various eluent compositions. For water-rich eluents, it is reasonable to assume that water is not taken up by the hydrophobic stationary phase and the immobilized eluent layer consists of the pure organic eluent (modifier). Thus, ViS ) VS ) (VR,i - VR,D2O)θiM

Figure 5. Comparison of the thermodynamic and kinetic void volumes for acetonitrile (A) and methanol (B): (b) thermodynamic void volume, V0; (2) kinetic void volume, VM; (() retention volume of thiourea.

or on the stationary phase is constant throughout the entire composition range2,6 and equal to that observed in the range 0.5 e θiM e 0.8 or that water is not retained by the hydrophobic bonded phase with water-rich eluents,23 that is, only the organic eluent component is taken up by the stationary phase. In the latter case, the retention volume of deuterated water would serve as an accurate measure of the volume of eluent in the

In the intermediate eluent composition range, ViSand VScan be determined from the linear region of the excess sorption isotherm and in organic-rich eluents ViS f VSas θiM f 1. Evaluation of Test Solutes as Dead Time Markers. In addition to deuterated water, various other solutes have been suggested as dead time probes. In order to determine the effect of the choice of solute for a dead time marker on the determination of absolute isotherm data, the retention volumes of thiourea and acetone were measured over the full range of eluent composition. These two solutes along with deuterated water have all been used as dead time markers in the literature. In Figure 4, the absolute volumes of acetonitrile and methanol in the stationary phase

Figure 6. Retention factors of tetrahydrofuran and artemisinin using V0 (b) and VM (2) in acetonitrile (A, C) and methanol (B, D). 3334

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(8)

Figure 7. Retention factor ki(VM) of acetone (A), tetrahydrofuran (B), and artemisinin (C) as a function of the absolute volume of eluent sorbed by the stationary phase: (b) acetonitrile; (O) methanol.

calculated using eq 1 with the retention volumes of the three solutes used as a measure of VMare illustrated along with the calculated line obtained from the results given in Table 1. Acetone is not a viable dead time marker for either of these systems at any eluent composition. With acetonitrile as an eluent component, thiourea produced low values for the calculated amount of acetonitrile in the stationary phase. The same is true in the case of the methanol eluent; however, at high methanol concentrations, the use of thiourea as a dead time marker produced a positive error in the calculated isotherm. These results illustrate the need for the measurement of excess isotherms for any sorbate (solute or eluent) when the data are collected over a wide range of eluent composition. Thermodynamic and Kinetic Void Volumes. The thermodynamic void volume was calculated from the retention volumes of the tracer eluent components. The kinetic void volume was calculated from the regression results from Table 1 and the measured retention volume of water in the range θiM e 0.4. The volume of mobile phase in the eluent composition range θiM g 0.5 was determined from the relation VM ) V0 - VS. The results of these calculations are illustrated in Figure 5. The retention

volume of thiourea was included in Figure 5 to assess the viability of this analyte as an unretained dead time probe to provide an accurate measure of the mobile-phase volume. The data for acetonitrile show that thiourea is not an accurate dead time marker for this system. The smallest error, ca. +4%, between the calculated mobile-phase volume and the retention volume of thiourea was observed at a volume fraction of 0.4. In the case of methanol, on the other hand, thiourea was a relatively accurate dead time marker over the composition range from 0.4 to 0.8. Throughout this composition range, the retention volume of thiourea was actually slightly less (e3%) than the kinetic void volume calculated from eq 4. This discrepancy was also observed in a previous study.9 The general conclusion would be that thiourea can serve as an adequate dead time marker with methanol as the eluent but only for organic rich eluents. Retention Factors of Test Solutes. In addition to the uptake of eluent as a function of composition, the limiting retention volumes of six additional test solutes were determined. The chromatographic systems were ternary with one component (test solute) at infinite dilution. The test solutes used were tetrahydrofuran, acetone, 3-methoxyphenol, 4-methoxy-2-nitroaniline, artemisinin, and methanol or acetonitrile depending upon the eluent. The retention factors of the test solutes were calculated using both the kinetic void volume (eq 5) and thermodynamic void volume (eq 6). The results for tetrahydrofuran and artemisinin are shown in Figure 6 in the form of a logarithmic plot. The results for the two different void volume calculations are similar for methanol eluent; however, the results differ significantly with acetonitrile, reflecting the greater extent of sorption of the acetonitrile eluent. In order to determine whether or not adsorbed eluent could act as a separate stationary phase and affect the retention of test solutes, the retention factors of the test solutes were plotted as a function of the absolute volume of acetonitrile or methanol taken up by the bonded packing. The results are shown in Figure 7. In each case, the retention factor of the test solutes decreased as the amount of eluent in the stationary phase increased. Thus, the uptake of eluent is not the decisive factor in the retention mechanism for the analytical solutes. CONCLUSIONS Numerous investigations,2,4,23,24 including the present study, have shown that both methanol and acetonitrile are commonly adsorbed on or absorbed in C18-bonded phases in RPLC systems. The volume of acetonitrile taken up by the stationary phase was about four times as much as methanol at the same eluent composition. The previous studies were based on the experimental results obtained from frontal analysis or concentration pulse chromatographic methods. The experimental technique of tracer pulse chromatography, however, provides a method for the comparison of both the thermodynamic and kinetic void volumes of RPLC columns. Currently, there are two principal methods to determine the kinetic void volume, viz., linear regression of excess volume (21) Schay, G. In Surface and Colloid Science; Wiley-Interscience: New York, 1969; Vol. II, pp 180. (22) Kazakevich, Y. V. J. Chromatogr., A 2006, 1126, 232–243. (23) Alvarez-Zepeda, A.; Martire, D. E. J. Chromatogr. 1991, 550, 285–300. (24) Gritti, F.; Guiochon, G. J. Chromatogr., A 2007, 1155, 85–99.

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data for eluents along with accurate measurement of the thermodynamic void volume or the assumption that the retention volume of an unretained solute is a true measure of VM. One method depends upon accurate assessment of stationary-phase parameters while the other depends only upon mobile-phase properties. These two methods have been compared using thiourea and acetone as the unretained markers. Acetone was not an accurate measure void volume. Thiourea could provide an estimate of the kinetic void volume but only under restricted conditions. The thermodynamic void volume determined from excess volume data was also accurate but only over a restricted composition range. The retention factor for all of the test solutes diminished as the absolute volume of eluent present in the stationary phase increased. Thus, it is not possible from the data to evaluate the Kazakevich multiphase model for the stationary phase in RPLC systems because the volume of eluent in the stationary phase is

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not a dominant factor in the retention of analytes for the systems investigated herein. ACKNOWLEDGMENT This research was supported by Grant CHE-0715094 from the National Science Foundation. The University of Mississippi provided funds for the instrumentation. SUPPORTING INFORMATION AVAILABLE Tables S-1 and S-2 with experimental retention volume data of eluent components and test solutes and calculated void volumes. This material is available free of charge via the Internet at http://pubs.acs.org.

Received for review January 18, 2010. Accepted March 9, 2010. AC100148B