Anal. Chem. 1980, 52,
2009-2013
2009
Effect of Eluent Composition on Thermodynamic Properties in High-Performance Liquid Chromatography Lane C. Sander and Larry R. Field’ Department of Chemistty,
BG-10, University of
Washington, Seattle, Washington 98 195
Chromatographic retention in high-performance liquid chromatography is lnvestlgaled thermodynamically for selected compounds on two mkroparticulate LC columns: pBondapak C,* column and Zorbax CN column. Thermodynamic solution property trends for solutes N,N-diethylaniline and isopropylbenzene are examined as a function of mobile-phase composition. Enthalpies and entropies of transfer (mobile to stationary phase) are calculated from retention data by evaluation of Van’t Hoff plots. For all cases examined, enthalpies of transfer are negative and increase with the percentage methanol In the eluent. The dependence of k’ upon values of AHo is shown to decrease with increasing nonpolar character of the eluent. Enthalpy-entropy compensation behavior is tested for varying mobile-phase compositions.
Chemically bonded stationary phases have found universal acceptance in high-performance liquid chromatography (HPLC) separations and continue to be the object of intense research (1-7). Versatility in separations, temperature stability, and long column lifetimes are a few reasons bonded phases have become so popular. Unfortunately, relatively little is understood about the mechanism of solute interaction with bonded stationary phases. Explanation of solute retention in “reversed-phase’’separations is usually described qualitatively through partitioning models or by use of the hydrophobic effect. Although the idea of a simple, unifying model for “reversed-phase’’ HPLC has great appeal, current studies tend to indicate that solute retention is a complex process dependent upon a number of factors. Liquid-liquid partitioning as a mechanism for bonded phases has serious limitations and is often discounted (3,8). The liquid-liquid partitioning model presupposes the existence of two immicible liquid phases. Solute concentration in each phase is governed thermodynamically by the distribution coefficient, K = (concentration of solute phase 1)/ (concentration of solute phase 2). By nature of the bond itself, bonded phases differ from ideal liquids. If the bonded phase is visualized as a collection of equal length alkyl chains, each with one end attached and one end free, deviations from normal solution behavior are t o be expected. The number of degrees of freedom for the bonded phase is substantially reduced over that of a true liquid, and as a consequence the stationary phase is more ordered. While a partitioning model may be a valid approach to understanding nonbonded, physically coated supports, its application to bonded phase supports leaves many questions unanswered. In recent years, use of the hydrophobic effect in reversedphase HPLC to explain solute-bonded phase interaction has received increasing attention (9, 10). Nonpolar molecules exhibit relatively large negative entropies of solution in aqueous solutions. This phenomenon has been attributed to an ordering of water molecules adjacent to the surface of the solute molecule (10). The hydrophobic effect can be described as the tendency of a nonpolar solute molecule to reduce its surface area exposed to water-either through association with 0003-2700/80/0352-2009$01 .OO/O
other nonpolar molecules or through removal from the solution by adsorption (3)-and thereby increase the entropy of the system. Horvath (9) and others (10, 11) contend that in reversed-phase HPLC, solute retention on the bonded phase is largely governed by these hydrophobic interactions. Determination of actual retention mechanisms in reversed-phase HPLC is a formidable problem and mu-h work remains to be done. Hemetsberger et al. investigateu effects of bonded-phase length (12) and structure (13) for several chemically bonded phases. Locke (14) related retention to solute solubility in the mobile phase, and Horvath e t al. (9) derived expressions for k’in terms of properties of the solute, the mobile phase and the bonded phase. Recently, Scott and Kucerna demonstrated that solutes interact with but do not displace a monolayer of organic molecules associated with the stationary phase (15). One of the first thermodynamic investigations was made by Knox and Vasvari (16). Knox plotted In k’ vs. 1/T for a group of compounds separated on Permaphase ETH and ODS columns. The resultant Van’t Hoff plots gave absolute enthalpies and relative entropies of transfer for the solutes. Since this early work, Guiochon and Horvath (3,11,17) have been instrumental in advancing our understanding of separation mechanisms through various thermodynamic considerations. This paper reports the results of an investigation into the thermodynamic behavior of selected compounds in reversed-phase HPLC. Thermodynamic solution property trends are examined as a function of eluent composition. The relative effect of A S o and AH” on k’ is discussed, and enthalpy-entropy compensation behavior is tested as a function of mobile-phase composition.
EXPERIMENTAL SECTION Instrumentation. A Spectra Physics (Santa Clara, CA) SP8000 liquid chromatograph employing a 254-nm fixed-wavelength detector, data collection system, and autoinjector was used. Column temperatures were regulated to 0.5 “C in a forced air oven. Two microparticulate columns were utilized: a 4.6 mm X 30 cm Waters (Milford, MA) pBondapak CI8column and a 4.6 mm X 25 cm DuPont (Wilmington, DE) Zorbax CN column. Reagents. Test samples were from the Chem Service (West Chester, PA) ministockroom reagent file and were used without further purification. Reagent grade methanol and distilled water were purified prior to use by distillation at a 1:l reflux ratio on a spinning band distillation apparatus. Ten-millimolar citric acid solutions were prepared from reagent grade citric acid (Mallinckrodt, St. Louis, MO). Procedure. Chromatographic retention characteristics of selected compounds were obtained through automated analysis. The liquid chromatograph was programmed t o vary the mobile-phase composition from 20 to 100% methanol (10 mM citric acid was added to both methanol and water phases) in consecutive 5 70 increments. With each change in mobile-phase composition, the column was permitted to reequilibrate by flushing with 15 void volumes of eluent at the new composition. Replicate analyses were made at each composition and temperature. Column temperatures were set at the beginning of a series of analyses and were held constant as the mobile-phase composition was varied. Each solute was chromatographed independently. Ten-microgram (10 WLat 1 ppt) injections were used at a mobile-phase flow rate 0 1980 American Chemical Society
2010
ANALYTICAL CHEMISTRY, VOL. 52,NO. 13,NOVEMBER 1980 A
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Figure 1. Solute retention vs. mobilephase composeion (waterhethanol)for N,Ndiethylanaline and isopropylbenzene on Zorbax CN and pbndapak C,8 columns: (0)299 K; ( X ) 308 K; (A)333 K.
of 2 mL/min. Retention times were measured by the data system. Void volumes were measured at each solvent composition and were determined from the refractive index change resulting from injection of water or methanol. Entropies and enthalpies of transfer were calculated through linear regression analysis of Van’t Hoff plots. AU graphs and calculations were prepared by computer programs written in FORTRAN IV language.
RESULTS AND DISCUSSION T h e measurement of thermodynamic quantities in HPLC is relatively new and is still fairly controversial ( 3 ) . Solute retention is usually expressed in terms of the capacity factor, k’, which is defined as (grams solute in stationary phase)/ (grams solute in mobile phase). The capacity factor is proportional to the equilibrium constant K and can be written
k’ = @K (1) The constant of proportionality (6)is the phase ratio (volume stationary phase)/(volume mobile phase). Gibbs free energy is related to the equilibrium constant in eq 2, and eq 3 is the
AGO = -RT In K
(2)
AG” = AH” - TAS”
(3)
familiar relation relating standard enthalpies and entropies to free energy. On combination of eq 1-3, the capacity factor can be expressed in terms of standard enthalpies and entropies of transfer from mobile to stationary phase (eq 4). If AHo
I n k ’ = -AHo/RT+ A S ” / R
+ In @
(4)
and ASo are independent of temperature over the temperature interval of interest, a plot of In k’ vs. 1/T (the classical “Van’t
Hoff plot”) will be linear. While the slope of this line gives standard enthalpies of transfer, standard entropies of transfer are calculated from the intercept and are thus dependent on the value of the phase ratio. Numerical values for the phase ratio may be estimated from physical constants of the packing material. Knox estimated 4 to be for a polymeric, pellicular packing (16). Phase ratios for totally porous, microparticulate silica packings would be expected to differ considerably from this value because of the larger surface areas of these supports. In order to estimate phase ratios for the columns used in this study, we constructed physical models of the bonded phases using manufacturer’s data regarding silanol surface coverage and percent carbon loading. Volumes of the bonded phases for the Zorbax CN column and pBondapak C18column were estimated from these models, and the corresponding phase ratios were calculated: C#J = 1 / 4 2 for the CN column; C#J = 1/2.6 for the CIBcolumn. Recent pycnometer measurements (18) of phase ratios for similar bonded phases compare favorably with the values reported here. It is important to note that AHovalues are independent of the phase ratio. In addition, any uncertainity in the phase ratio affects ASo values equally, and thus trends in A S o as a function of eluent composition are unaffected. It is estimated that uncertainty in the calculated phase ratios would result in a maximum of h3.6 cal/mol offset in these trends. Unusual retention behavior has been observed (19) for NJV-diethylaniiineon a Zorbax CN column (Figure 1A). That amines are not “well-behaved’’ in certain chromatographic systems has previously been observed (20-22). In order to study this unusual chromatographic behavior, we selected Nfl-diethylaniline and a non-nitrogen-containing compound
ANALYTICAL CHEMISTRY, VOL. 52, NO. 13, NOVEMBER 1980
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Percent m e t h a n o l Percent methanol Figure 2. Standard enthalpies of transfer (mobile to stationary phase) as a function of mobile-phase composition, of similar structure, isopropylbenzene, as model probes for comparisons. It was hoped that both the nonpolar character and the more normal retention behavior of isopropylbenzene (Figure 1B) would increase our understanding of the peculiar retention behavior observed for N,N-diethylaniline on the Zorbax C N column. More specifically, it was hoped that comparison of thermodynamic trends for the two probe compounds might help to explain solute-column interactions based on the different polarities of the solute molecules. The unusual behavior of N,N-diethylaniline on the Zorbax C N column is characterized by increased retention at low and high percentages of methanol and shows a minimum in k' near 60%. This behavior was observed at 299,308, and 333 K. As expected, retention decreased with increasing temperature. Knox and Jurand found that addition of a small quantity of an organic acid to the mobile phase reduced retention and improved peak shape of certain amines (21). In our initial studies, N,N-diethylaniline exhibited long retention times on the C N column. p H adjustment of the mobile phase with citric acid (10 mM, pH 2.6) reduced k' to an acceptable level. Similar results have also been obtained for 10 mM mobilephase solutions of phosphoric acid. In this work, citric acid was added to the mobile phase in all experiments. The observed retention behavior of Nfl-diethylaniline may be the result of several possible interactions. One explanation is that N,N-diethylaniline shows reversed-phase behavior at compositions less than 60% but, due to its polarity, interacts with the nitrile moiety in a quasi-normal-phase mode for higher methanol concentrations. Another explanation involves a mixed retention mechanism resulting from both silanol group and solute-bonded phase interactions. At a p H of 2.6, N,Ndiethylaniline is protonated (pK, = 6.61), and interactions responsible for silanol-amine hydrogen bonding are reduced. Retention under these conditions would result primarily from
conventional solute-bonded phase interactions (i.e., decreasing k' with increasing organic character of the mobile phase). However, at high methanol concentrations, a reduction in acid ionization would lead to decreased amine protonation and thus increased hydrogen bonding with the exposed silanol groups. Isopropylbenzene under either of these conditions would not exhibit the observed increase in retention a t high methanol concentrations. As can be seen in Figure lB, isopropylbenzene exhibited the more conventional retention behavior expected. Similarly, retention of both isopropylbenzene and N,N-diethylaniline on a Waters pBondapak CIScolumn decreased with increasing methanol composition (Figure 1C,D). Entropies and enthalpies of transfer (mobile to stationary phase) were calculated for each of the cases. Figure 2 shows trends in AHo and Figure 3 shows trends in ASo. One observation is immediately apparent. In each instance enthalpies of transfer are negative and values increase with increasing methanol concentration. Thus, transfer of the solute from the mobile phase to the stationary phase becomes enthalpically less favored at higher concentrations of methanol and results in a decrease in solute retention. In Figure 2D, enthalpies of transfer for isopropylbenzene on the pBondapak CIScolumn are consistently lower than for the other cases examined (Figure 2A-C). This behavior can be explained since interactions between a nonpolar solute and a nonpolar stationary phase are expected to be stronger than for solute-column combinations of dissimilar polarity. Entropies of transfer differed greatly for the cases examined. However, most ASo values are negative, and this supports the idea that the solute is more ordered on the stationary phase than in the mobile phase. Interestingly, this tendency decreases with increasing methanol concentration for the N,Ndiethylaniline solute. Associations of the N,N-diethylaniline
2012
ANALYTICAL CHEMISTRY, VOL. 52, NO. 13,NOVEMBER 1980
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molecules with eluent molecules should become more difficult with decreasing polarity of the solution, i.e., as the percent methanol is increased. An increase in the mutual association of solute molecules in the mobile phase would thus explain the positive, increasing trend of AS" values observed. An interesting observation can be made by comparing trends in AH"and AS" for N,N-diethylaniline on the Zorbax CN column. Both enthalpies and entropies of transfer are seen to increase with the percentage of methanol in the mobile phase. Since AH" and ASo terms in eq 4 (-AH"/RT, A S o / R ) are of opposite sign, the contribution made to k' by the ASo term increases with the percentage methanol in the eluent. From comparison of magnitudes of the calculated AH" and AS" terms, it can be seen that enthalpies of transfer are of primary importance a t low and moderate methanol concentrations and only at 80% methanol does the contribution of the ASo term surpass that of the AH" term in eq 4. A similar argument can be made for the pBondapak C18column. From trends in enthalpies and entropies of transfer for N,N-diethylaniline on this column, the importance of AS" to retention is seen to increase with the percentage methanol. However, in this case a comparison of the magnitude of ASo and AH" terms shows the AH" term to be the major contributor to retention, even at high methanol concentrations. Thus for N,N-diethylaniline, it appears that entropy plays an increasing role in retention as the organic composition of the eluent increases. Linear relations between changes in enthalpy and entropy have been observed for a variety of processes involving aqueous solutions of low molecular weight solutes. This behavior is labeled enthalpy-entropy compensation and is believed to result from solute-induced free volume changes in liquid water (23). Melander, Campbell, and Horvath (24) recently explored enthalpy-entropy compensation in reversed-phase chroma-
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tography. Compensation behavior was observed for a variety of solutes with and without modifiers in the mobile phase. It has been suggested by Melander that the slope of the enthalpy-entropy plot, called the compensation temperature, is constant for processes exhibiting similar interaction mechanisms. Thus, chromatographic retention of a solute (as a function of eluent composition) would be expected to occur from an unchanging interaction mechanism if that solute displayed enthalpy-entropy compensation over the range of varying composition. The following equation is used in the calculation of the compensation temperature (8) where T is the temperature at which the measurement was made and R is the gas law constant. A plot of In k' vs. - ( A H " / R ) should yield a line of slope 1 / T - l/p. Enthalpy-entropy compensation behavior was tested for each solute/column set for a wide range of mobile-phase compositions, typically 20-100% methanol. In k' was plotted against -AI-fo a t the different mobile-phase compositions. Enthalpy-entropy compensation plots for both N,N-diethylaniline and isopropylbenzene demonstrate compensation behavior on the KBondapak C18 column. Correlation coefficients for the two plots are 0.860 and 0.993, respectively. The fact that each plot is linear suggests that the solute-bonded phase interaction mechanism for the pBondapak column remains constant for varying eluent composition. Enthalpyentropy compensation was not observed on the CN column. A correlation coefficient of 4.266 was obtained for the NJVdiethylaniline sample and -0.380 for the isopropylbenzene sample. That N,N-diethylaniline did not show compensation behavior might be expected, as this is consistent with the mixed mechanism (involving exposed silanol groups) postulated earlier.
Anal. Chem. 1880, 52, 2013-2018
ACKNOWLEDGMENT
(10) Karger, Barry L.; Gant, Russel J.; Hartkoph, Arleigh; Weiner, Paul H. J . Chromatoor. 1976. 728. 65-78. (1 1) Colin, Hen&; Guiochon, deorges J . Chromafogr. 1978, 758, 183-205. (12) Hemetsberger, H.; Maasfeld, W.; Ricken, H. Chromatcgraphia 1976, 9 , 303-3 10. (13) Hemetsberger, H.; Behrensmeyer, P.; Henning, J.; Ricken, H. Chromatographia 1979, 72, 71-76. (14) Locke. David C. J . Chromatogr. Sci. 1974, 72, 433-437. (15) Scott. R. P. W.; Kucerna, P. J . Chromatogr. 1977, 742, 213-232. (16) Knox. John H.; Vasvari, Gabor J . Chromatogr. 1973, 8 3 , 181-194. (17) Hwvath, Csaba; Mebndec, Wayne; Molnar, Imre Anal. Chem. 1977, 49, 142-1 54. (18) Sander, Lane C.; Field, Larry R., unpublished work. (19) Parris, Norman E. 1. duPont de Nemours 8 Co., Inc., Wllmlngton, DE, personal comunicatlon, Dec 18, 1978. (20) Sokolowskl, A.; Wahlund, K. G. J . Chromatogr. 1980, 789, 299-316. (21) Knox, J.; Jurand, J. J . Chromatogr. 1977, 742, 651-670. (22) Twkchett, P.; Moffat, A. J . Chromatogr. 1975, 7 7 7 , 149-157. (23) Lumry, Rufus, Rajender, Shyamala Biopolymers 1970, 9 , 1125-1227. (24) Melander, Wayne; Campbell, David E.; Horvath, Csaba J. Chromatogr. 1978, 158, 215-225.
The authors wish to thank Spectra Physics Inc. for the generous loan of the SP8000 liquid chromatograph, and Dupont, Inc., for a gift of the Zorbax CN column. Special thanks are also due to Dave Herman for his helpful discussions and ideas on the subject.
LITERATURE CITED (1) Cox, C. 0. J . Chromatogr. Sci. 1977, 385-392. (2) . . Colin. Henri: Ward. Norman: Guiochon. Georaes J . Chromatwr. 1978. 749, 169-197. (3) Horvath, Csaba; Melander. Wayne J . Chromatcgr. Sci. 1977, 75, 393-404. (4) Unger, K. K.; Becker, N.; Roumeliotls, P. J . Chromatogr. 1976, 725, 115- 127. (5) Roumeliotis, P.; Unger, K. K. J. Chromatogr. 1978, 749, 211-224. (6) Karch, Karl; Sebestian, Imrlch: Halasz, Istvan J . Chromatogr. 1978, 722, 3-16. (7) Hennion, M. C.; Picard, C.; Cam,M. J. Chromatogr. 1978, 766,21-35. (8) Simpson, C. F. “Practical High Performance Liquid Chromatography”, 1st ed.;Heyden and Son Ltd.: London, 1976; Chapter 7. (9) Horvath, Csaba; Melander, Wayne; Molnar, Imre J. Chromatogr. 1976, 725, 129-156.
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2013
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RECEIVED for review February 29,1980. Accepted August 4, 1980.
Chromatographic Properties of Silica-Immobilized Antibodies J. Richard Sportsman and George S. Wilson’ Department of Chemistry, University of Arizona, Tucson, Arizona 85779
Antibodies against protein antigens have been immobilized on silane-treated porous glass and used in a technique designated “high-performance lmmunoaffinity chromatography” (HPIC). A theory has been developed for HPIC which adequately describes the blnding of antigen by immobillred antibody in terms of an apparent binding constant, K’, whose value is flow-rate dependent. The concentration and heterogeneity of blnding sites on the chromatographic column also are successfully predicted by the theory; ail parameters are shown to be in agreement with those determined by batch methods. The suitability of porous silica as a support for the immobiliratlon of proteins and the possibility of antibody fractionation are discussed.
T h e use of antibodies immobilized on insoluble supports for immunoassays and protein purification is now common practice. In the case of the radioimmunoassay (RIA), an immobilized antibody, or immunosorbent, enables a more convenient separation of antibody-bound antigen from unbound antigen; more important is the fact that the precision and sensitivity of the assay is noticeably improved over homogeneous RIA methods ( I , 2). The proliferation of methods for affinity chromatographic purification of innumerable substances has also resulted in the routine use of immunosorbents for these purposes. Comparatively little work has been done in an attempt to better understand the kinetics and thermodynamics of the reactions of antigens with specific immunosorbents ( 3 , 4 ) . Of particular interest is the question of whether immobilization affects the characteristics of immunochemical reactions. Antibodies against protein antigens have been shown to retain considerable binding capacity when attached to gly0003-2700/80/0352-2013$01 .OO/O
cerylpropylsilane (GOPS) derivatives of silica particles and used in a high-pressure liquid chromatographic (HPLC) configuration (5). This appeared to offer a convenient method for studying the reaction of antigen with immobilized antibody, since when so configured, the immunosorbent is reusable and need not be handled or transferred. Furthermore, the HPLC configuration enables one to quantitate the distribution of antigen between solution and binding site by spectrophotometric or fluorometric detection in a flow cell. Finally, it becomes quite simple to vary the conditions of the antigenantibody interaction by adjustment of the mobile-phase composition. Porous silica was chosen as a support because of its low cost and high dimensional stability. It was necessary to use 10 pm diameter particles because the method described below requires maximum surface area and minimum volume. The use of silane-treated porous glass for immobilization of proteins has not generally been as widespread as that of agarose, dextran, and other organic polymers owing largely to some unfavorable reports regarding the supposed lack of stability of protein ligands when attached to silica surfaces (6). Additionally, the tendency of such surfaces to irreversibly absorb proteins has earned porous glass in general a bad reputation (9, in spite of recent work which shows t h a t diol bonded phases on silica provide a suitably deactivated surface for protein chromatography (8, 9). For this study we investigated the binding of two antigens, human immunoglobulin G (IgG) and fluorescamine-labeled beef insulin, by their respective antibodies immobilized on silica. We report the results of experiments which demonstrate that under the appropriate conditions, the binding of an antigen by a “high-performance i m m u n o a f f i n i t y chromatographic” (HPIC) column can be described in terms of an apparent binding constant, which can be related to values 0 1980 American Chemical Society
