Adsorption Mechanisms and Effect of Temperature in Reversed-Phase Liquid Chromatography. Meaning of the Classical Van t Hoff Plot in Chromatography

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1 Anal. Chem. 2006, 78, Adsorpton Mechansms and Effect of Temperature n Reversed-Phase Lqud Chromatography. Meanng of the Classcal Van t Hoff Plot n Chromatography Fabrce Grtt and Georges Guochon* Department of Chemstry, Unversty of Tennessee, Knoxvlle, Tennessee , and Dvson of Chemcal Scences, Oak Rdge Natonal Laboratory, Oak Rdge, Tennessee The effect of temperature on the adsorpton and retenton behavors of a low molecular weght compound (phenol) onac 18 -bonded slca column (C 18 -Sunfre, Waters) from aqueous solutons of methanol (20%) or acetontrle (15%) was nvestgated. The results of the measurements were nterpreted successvely on the bass of the lnear (.e., overall retenton factors) and the nonlnear (.e., adsorpton sotherms, surface heterogenety, saturaton capactes, and equlbrum constants) chromatographc methods. The confrontaton of these two approaches confrmed the mpossblty of a sound physcal nterpretaton of the conventonal Van't Hoff plot. The classcal lnear chromatography theory assumes that retenton s determned by the equlbrum thermodynamcs of analytes between a homogeneous statonary phase and a homogeneous moble phase (although there may be two or several types of nteractons). From values of the expermental retenton factors n a temperature nterval and estmates of the actvty coeffcents at nfnte dluton n the same temperature nterval provded by the UNIFAC group contrbuton method, evdence s provded that such a retenton model cannot hold. The classcal Van't Hoff plot appears meanngless and ts lnear behavor a mere accdent. Results from nonlnear chromatography confrm these conclusons and provde explanatons. The retenton factors seem to fulfll the Van't Hoff equaton, not the Henry constants correspondng to the dfferent types of adsorpton stes. The saturaton capactes and the adsorpton energes are clearly temperature dependent. The temperature dependence of these characterstcs of the dfferent assorpton stes are dfferent n aqueous methanol and acetontrle solutons. A better understandng of the mechansm(s) of adsorpton n RPLC 1-4 would help to mprove the analytcal performance of * To whom correspondence should be addressed. Fax: E- mal: guochon@utk.edu. (1) Horváth, Cs.; Melander, W. R.; Molnar, I. J. Chromatogr., 1976, 125, 129. (2) Guochon, G.; Golshan-Shraz, S.; Katt, A. M. Fundamentals of Preparatve and Nonlnear Chromatography; Academc Press: Boston, MA, (3) Dorsey, J. G., Dll, K. A. Chem. Rev. 1989, 89, 331. chromatography n envronmental, food, bologcal, and pharmaceutcal analyses 5 by leadng to the development of better statonary phases allowng faster separatons and lower detecton lmts. We showed recently how the results of measurements that are classcal n nonlnear chromatography shed new lght on these mechansms and reveal unexpected phenomena n RPLC. 6 Frst, the surfaces of adsorbents are heterogeneous. 7-9 Ths fact explans the peak talng observed at even moderate sample szes, 10 a talng that has a nefarous mpact on the separaton and the detecton of analytes. The classcal models used to nterpret the dependence of the retenton factor at nfnte dluton, k, on the moble-phase composton and the temperature are the lnear solvent strength model (LSSM) and the Van't Hoff plot, respectvely. The LSSM assumes a homogeneous statonary phase and plots ln k versus the volumetrc fracton, φ, of the organc solvent whle the classcal Van't Hoff plots (ln k versus (1/T)) mples that there s a sngle retenton mechansm. So, both approaches mply that the statonary phase,.e., the adsorbent surface, s homogeneous, whch t s not. 6-9 These models are emprcal and do not reflect the true retenton model of the compounds n RPLC. We showed recently that a careful analyss of the adsorpton data of neutral and onzable low-molecular-weght compounds (phenol, caffene, naphthalene sulfonate, propranololum chlorde) on conventonal RPLC columns demonstrates the coexstence of at least two and a maxmum of four dstnct types of adsorpton stes. 11,12 We showed also that the mechansms of adsorpton of neutral molecules from aqueous solutons of methanol and acetontrle are qute dfferent. 13 Fnally, we showed that the adsorpton models of onzable compounds n the presence of counterons depend consderably on the valence of ths counteron snce a convex upward, an S-shaped, and a convex downward (4) Wlson, N. S.; Nelson, M. D.; Dolan, J. W.; Snyder, L. R.; Wolcott, R. G.; Carr, P. W. J. Chromatogr., A 2002, 961, 171. (5) Neue, U. D. HPLC Columns. Theory, Technology, and Practce; Wley-VCH: New York, (6) Grtt, F.; Guochon, G. J. Chromatogr., A 2005, 1099, 1. (7) Grtt, F.; Guochon, G. Anal. Chem. 2003, 75, (8) Grtt, F.; Guochon, G. J. Chromatogr., A 2004, 1028, 105. (9) Grtt, F.; Guochon, G. Anal. Chem. 2005, 77, (10) Grtt, F.; Guochon, G. J. Chromatogr., A 2004, 1028, 75. (11) Grtt, F.; Guochon, G. J. Chromatogr., A 2006, 1103, 43. (12) Grtt, F.; Guochon, G. J. Chromatogr., A 2006, 1103, 57. (13) Grtt, F.; Guochon, G. Anal. Chem. 2005, 77, Analytcal Chemstry, Vol. 78, No. 13, July 1, /ac CCC: $ Amercan Chemcal Socety Publshed on Web 06/09/2006

2 sotherms were observed when the valence of the counteron was one, two, and three, respectvely. 14 In all these cases, lnear chromatography was clueless to dstngush between these dfferent behavors because t measures the mere retenton tme, whch s smply the sum of the contrbutons of the dfferent retenton mechansms to the Henry s constant. In our prevous work, we focused on the effects of the organc solvent, the supportng salts, and the buffers on the adsorpton propertes of the statonary phase n RPLC. In ths work, we followed a smlar approach and performed nonlnear chromatography experments nvolvng the effects of temperature on the adsorpton behavor of neutral compounds on RPLC columns. It s well known that retenton factors almost always decrease wth ncreasng temperature. The questons that we want to answer are, Why? What does cause ths decrease? How do the saturaton capactes and the equlbrum constants of adsorbates change wth ncreasng temperature? A smlar study was done earler on an end-capped C 18 -bonded column (Symmetry, Waters). 15 It showed that the adsorpton of phenol followed a two-ste, b-langmur sotherm model behavor and that the number of the lowadsorpton energy stes q S,1 and the equlbrum constant of the hgh-adsorpton stes b 2 decrease rapdly whle the number of hghadsorpton energy stes q S,2 and the equlbrum constant of the low-adsorpton energy stes b 1 reman nearly constant when the temperature ncreases. So, both contrbutons to k ) F q S b decrease wth ncreasng temperature, but for dfferent reasons. These results suggest that the nterface structure between the bulk moble phase and the top of the bonded layer, where the chans have a hgh moblty, s qute senstve to temperature whle the nner structure of the bonded layer, where the chans have a lmted moblty, was less senstve to temperature change. In ths work, we consder the behavor of the same analyte (phenol) wth dfferent moble phases (both methanol and acetontrle were used as organc solvents), on a dfferent C 18 -bonded column (Sunfre, Waters) provded by the same manufacturer. We nvestgate the detals of the retenton mechansm of phenol on the dfferent types of adsorpton stes wth dfferent moble phases (contanng methanol or acetontrle as organc modfer). The valdty of applyng the classcal Van't Hoff law to chromatographc data s then dscussed, based on a comparson between the nterpretaton of the data measured n lnear and n nonlnear chromatography. THEORY Determnaton of the Adsorpton Isotherm Data by Frontal Analyss (FA). Frontal analyss 2,16,17 was used to measure the sngle-component adsorpton sotherm data used n ths work. The moble-phase composton was selected so that the retenton of the probe was suffcently large to permt the retenton data to be measured wth accuracy wthn a reasonable tme. The determnaton of the probe amount that s adsorbed on the column at equlbrum wth a soluton of known concentraton s explaned (14) Grtt, F.; Guochon, G. Anal. Chem. 2004, 76, (15) Km, H.; Grtt, F.; Guochon, G. J. Chromatogr., A 2004, 1049, 25. (16) Schay, G.; Szekely, G. Acta Chem. Hung. 1954, 5, 167. (17) James, D. H.; Phllps, C. S. G. J. Chem. Soc. 1954, n detal elsewhere. 18 It requres the precse measurement of both the extracolumn volume and the hold-up column volume V M. The frst one was measured from the retenton tme of the nflecton pont of the breakthrough curve recorded wthout a chromatographc column, the second from pycnometrc measurements, n whch methanol and dchloromethane were used as the two solvents, wth F CH3OH ) g/cm 3 and F CH2Cl 2 ) g/cm 3. The column hold-up volume s gven by m CH2 Cl 2 - m MeOH V M ) F CH2 Cl 2 -F CH3 OH where m CH2Cl 2 and m MeOH are the masses of the column when flled wth dchloromethane and methanol, respectvely. The general equaton that gves the amount q* of sample adsorbed per unt volume of adsorbent s smply derved from the mass balance equaton wrtten between the moments when the sample soluton at concentraton C 0 enters the column and when the adsorbent at the outlet of the column (x ) L) s at equlbrum wth ths sample soluton: q*(c 0 ) ) where V C s the column tube volume, F v the moble-phase flow rate, and C(t) the concentraton profle recorded at the column outlet (x ) L). t M s defned as the rato (V M /F v ). The precson of the measurements of q*(c 0 ) s dscussed later (see Precson of the FA Data). Adsorpton Isotherm Models. Two dfferent models of adsorpton sotherms were found useful n ths study, dependng on whether methanol or acetontrle was used as the organc modfer. The adsorpton sotherm models that ft best the adsorpton data of phenol on end-capped C 18 -bonded columns wth methanol-water moble phases are the b- Langmur 7 or the tr-langmur 8,20 model that both characterze adsorpton on a heterogeneous surface. The equaton of the latter model s q* ) q S,1 b 1 C 1 + b 1 C + q S,2 where q S,1, q S,2, q S,3, b 1, b 2, and b 3 are the saturaton capactes and the adsorpton-desorpton constants of the three types of stes. For the former model, q S,3 ) 0. The sotherm model that best accounts for the adsorpton data of neutral compounds from acetontrle-ater mxtures on RPLC columns s the BET-Langmur sotherm model. 13 The Langmur term descrbes adsorpton on the hgh-energy stes (monolayer adsorpton) and the BET term descrbes the multlayer adsorpton of the compounds on the low-energy adsorpton stes. (1) F v V C - V M tm [C0 - C(t)] dt (2) b 2 C 1 + b 2 C + q b 3 C S,3 1 + b 3 C (3-A) (18) Grtt, F.; Patkowsk, W.; Guochon, G. J. Chromatogr., A 2002, 978, 81. (19) Grtt, F.; Guochon, G. J. Chromatogr., A 2005, 1097, 98. (20) Grtt, F.; Guochon, G. J. Chromatogr., A 2004, 1043, 159. Analytcal Chemstry, Vol. 78, No. 13, July 1,

3 The equaton of ths model s b S C q* ) q S,1 (1 - b L C)(1 - b L C + b S C) + q b 2 S,2 1 + b 2 C (3-B) where b S and b L are the adsorpton-desorpton constants of the adsorbate on the surface of the adsorbent and on a layer of adsorbate molecules, respectvely. Fttng the Isotherm Data to the Isotherm Models. The adsorpton data derved from the FA method were drectly ftted to the adsorpton sotherm models lsted above, usng nonlnear regresson analyss. Each squared resdual was weghed by the factor (1/q exp2 ), to avod dscrmnatng the data ponts n favor of the hgh concentraton ones. It was verfed that the sotherm parameters obtaned were ndependent of each other. Calculaton of the Adsorpton Energy Dstrbuton (AED). The adsorpton energy dstrbuton or relatonshp between the surface area occuped by the adsorpton stes of type,.e., q S,, and the logarthm of the adsorpton-desorpton constant b was calculated usng the program developed by Stanley et al. and mplementng the expectaton-maxmzaton method. 21 The detal of the procedure s gven elsewhere. 6 The program assumes that the local sotherm follows Langmur sotherm model behavor. The overall sotherm s the convoluton of the local Langmur sotherm and the energy dstrbuton. In the case of adsorpton from acetontrle solutons, however, the overall sotherm s a BET- Langmur model because of adsorbate-adsorbate nteractons. In ths case, the overall sotherm cannot be deconvoluted nto a dstrbuton of Langmur sotherms and the program does not apply for the determnaton of the AED of phenol. EXPERIMENTAL SECTION Chemcals. The moble phases used n ths work were aqueous solutons of methanol and acetontrle wth concentratons of 20 and 15% (v/v), respectvely. Water, methanol, and acetontrle were of HPLC grade, purchased from Fsher Scentfc (Far Lawn, NJ). Pror to ther use, the solvents were fltered on an SFCA flter membrane, 0.2-µm average pore sze (Suwannee, GA). Phenol, the only solute used, was obtaned from Aldrch (Mlwaukee, WI). Columns. The column used n ths study (Sunfre-C 18 ) was gven by the manufacturer (Waters, Mlford, MA). The tube dmenson s mm. The man characterstcs of the packng materal are summarzed n Table 1. The column porosty was measured by pycnometry. Apparatus. The perturbaton sgnals and the overloaded band profles were acqured usng a Hewlett-Packard (now Aglent Technologes, Palo Alto, CA) HP 1100 lqud chromatograph. Ths nstrument ncludes a multsolvent delvery system (volume of each tank, 1 L), an autosampler wth a 250-µL sample loop, a UVvsble dode array detector, a column thermostat, and a data staton. The extracolumn volumes are and ml, as measured from the autosampler and from the pump system, respectvely, to the column nlet. All the retenton data were corrected for these contrbutons. The flow rate accuracy was (21) Stanley, B. J.; Balkowsk, S. E.; Marshall, D. B. Anal. Chem. 1994, Table 1. Physcochemcal Propertes of the RP-C 18 Columns Provded by the Manufacturer (Waters) C18-Sunfre (Waters) column dmenson (mm mm) partcle sze (µm) 5 mesopore sze (Å) 90 specfc surface area (m 2 /g) 349 bondng process monomerc carbon content (%) surface coverage (µmol/m 2 ) 3.85 total porosty b external porosty a end-cappng yes b Estmated from pycnometrc measurements (MeOH/CH 2Cl 2). a Estmated from nverse sze excluson chromatography measurements (polystyrene/thf). controlled by pumpng the pure moble phase at 295 K and 1 ml/ mn durng 50 mn, from each pump head successvely, nto a volumetrc glass of 50 ml. The relatve error was less than 0.1%, so we estmate the long-term accuracy of the flow rate at 1 µl/ mn at flow rates around 1 ml/mn. The temperature was controlled wthn (1 K. Precson of the FA Data. The accuracy of the measurements of the amount adsorbed, (.e., the dfference between the measured and the true values) s lmted by the precson of the measurements of (1) the flow rate, F v, delvered by the HPLC pump system ((0.4% for our HP1090 apparatus), (2) the volume of the column tube, V C (accordng to the manufacturer, the relatve standard devaton of the nternal volume of these stanless steel tubes s 0.5% around the value correspondng to ther average length, 150 mm, and nner dameter, 4.6 mm), and (3) the holdup volume, V M (accordng to the results of the pycnometc measurements, the error on V M s 0.4%). The error made on the ntegral term n eq 2 s much less mportant and can be neglected. It depends on the precsons on the concentraton, C 0, of the mother soluton of the sample n the moble phase and on the flow rate rato of the streams of pure moble phase and mother soluton. The mother soluton was prepared by weghng the sample (precson of the balance, ( g, lowest mass weghed, 0.5 g) and measurng the volume of moble phase wth a 100-mL volumetrc flask (precson, (0.05%). The error due to the flow rate mxer s less than 0.1%. Accordngly, an error calculaton shows that the relatve error made on the expermental values of q* s less than 2.5%. Most mportantly, ths error s systematc and remans the same for all values of the concentratons of the streams used n a set of FA measurements. Ths fact s consstent wth the smoothness of the plots of the expermental adsorpton data that exhbt no nose over the whole range of concentratons. Because the error made on the FA measurements s systematc and not random, the precson of the parameters of the adsorpton sotherm model s always good. It vares between 1 and 10%. Hence, any varaton of an sotherm parameter that s lesser than 10% from one temperature to another cannot be consdered as sgnfcant. On the other hand, an ncreasng or a decreasng trend of ths parameter wth an ampltude that exceeds 10% over the temperature range studed ( K) has defntely a physcal meanng Analytcal Chemstry, Vol. 78, No. 13, July 1, 2006

4 The hgh degree of precson of the FA method was demonstrated recently. 19 It was shown that the random error made durng a complete set of FA measurements s so small that selectng only 6 data ponts out of a set of 26 affects the numercal values of the sotherm parameters by less than a few percent f the selected data ponts cover the whole range of moble-phase concentratons. Ths s due to the mplementaton of the systematc expermental protocol that we have establshed durng the last four years. 6 RESULTS AND DISCUSSION In the followng secton, we assume that the retenton of the analyte s based on ts equlbrum dstrbuton between a moble and a statonary phase havng volumes V M and V S, respectvely. In the secton on the Case of a Homogeneous Statonary Phase, the statonary phase s assumed to be a sngle, homogeneous phase whle, n the secton on the Case of a Heterogeneous Statonary Phase, t s assumed to consst n two mmscble homogeneous phases. The statonary phases are modeled as pure lqud octadecane n the frst case or pure octadecane (phase 1) and an equmolar mxture of methanol and octadecane (phase 2) n the second case. Based on the thermodynamcs of phase equlbrum between the moble phase (modeled as methanolwater and acetontrle-water mxtures) and the statonary phase, the retenton factor k of phenol s predcted from a theoretcal pont of vew. The dervaton of the classcal Van't Hoff equaton s based on the valdty of such a dstrbuton model. The sutablty of the two models to account for the expermental results obtaned n the case studed was tested by comparng the varatons of the measured and the calculated retenton factors as a functon of the recprocal temperature. Fnally, the expermental retenton data of the analyte acqured by frontal analyss are analyzed n Interpretaton of the Adsorpton Isotherm Data wthout makng any assumpton. The adsorpton mechansm of phenol s dscussed based on the temperaturenduced varatons of the sotherm parameters (equlbrum constants and saturaton capactes). Ths approach gves a better understandng of the complexty of the retenton mechansm n RPLC than the mere measurement of the retenton factors and consderaton of ther Van't Hoff plot. Classcal Lnear Chromatography Approach and the Van't Hoff Plot. (1) Case of a Homogeneous Statonary Phase. The effect of temperature n analytcal chromatography has been wdely nvestgated. A popular nterpretaton of retenton mechansms conssts of assumng thermodynamc equlbrum of the analyte between the two phases of the chromatographc system. In RPLC, whch uses mostly C 18 -bonded slca phases, the statonary phase s a bonded layer smlar to lqud octadecane. The polar moble phase s an aqueous soluton of ether methanol or acetontrle. By conventon, the standard state of the analyte n ether phase s the pure analyte, wth a molar fracton equal to unty under normal pressure (P 0 ) 1 bar). Its actvty coeffcents are unty. The actvty coeffcents at nfnte dluton wll be estmated usng the UNIFAC group method calculatons descrbed n ref 22. The dstrbuton equlbrum of compound between the two phases s gven by wrtng the equalty of ts chemcal potentals µ n the two phases, hence: µ S ) µ M S µ 0,/ + RT ln γ S x S ) µ 0,/ + RT lnγ M x M (4) where the superscrpts S and M denote the statonary and the moble phases, respectvely, T s the temperature, and x and γ are the molar fracton and the actvty coeffcent of the analyte, respectvely. Note that the chemcal potental of the analyte n ts standard state s the same n both the statonary and the moble phases (pure state marked by the astersk /). In partcular, at nfnte dluton (.e., under lnear chromatography condtons), the equlbrum condton s wrtten where γ s the actvty coeffcent of the analyte at nfnte dluton. At nfnte dluton, the molar concentratons of the analyte, C S and C M S, are smply related to the molar fractons x and x M, respectvely, by ( x S C S) ( x S x M)eq, ) γ M, S, γ where V S,m and V M,m are the molar volume of the statonary and the moble phases, respectvely. The retenton factor, k, s the rato of the amounts of solute n the statonary and the moble phases 23 at nfnte dluton: where F s the phase rato of the chromatographc system and V S s the volume of octadecyl chans bonded to the surface of the slca. V S can be easly calculated from the physcochemcal propertes of the packng materal (Table 1). Note that the volume of the slca support should not be taken nto account because t s both mpermeable to the analyte and nert from a thermodynamc pont of vew. The Sunfre slca represents 77.3% of the overall wegh of the packng materal. Assumng a densty of slca equal to 2.12 g/cm 3 and that of the bonded layer equal to the densty of lqud octadecane, g/cm 3,1gofpackng materal s made of 0.36 cm 3 of slca and 0.29 cm 3 of hydrophobc layer. The volume of lqud phase V M was measured by pycnometry and s equal to 1.53 cm 3. The volume of bonded phase V S n the Sunfre- C 18 column s then 0.43 cm 3. In eq 7, H s the Henry s constant or smply the rato of the analyte concentratons n the statonary and the moble phases at equlbrum. Hence, the Van t Hoff plot equaton (5) ) V S,m and ( x M ) V M,m (6) C M) k ) V S V M ( C S ) FH (7) C M)eq, (22) Polng, B. E.; Prausntz, J. M.; O Connell, J. P. The propertes of gases & lquds, 5th ed.; McGraw-Hll, Inc., New York, (23) Gddngs, J. C. Unfed Separaton Scence; John Wley & Sons: New York, Analytcal Chemstry, Vol. 78, No. 13, July 1,

5 can be wrtten as k ) F V M,m γ M V S,m γ S (8) It s now possble to test the thermodynamc consstency of the chromatographc results by plottng the followng functon as a functon of the temperature: γ S γ M k ) φ (9) wth φ ) (V S /V M )(V M,m /V S,m ) ) (N S /N M ). Note that φ s smply the rato of the number of moles of statonary phase, N S (octadecane), to the number of moles of water, methanol, or acetontrle, N M, present n the column vod volume. N S s ndependent of the temperature, and N M slghtly decreases wth ncreasng temperature snce the molar volume of the lqud phase ncreases wth ncreasng temperature. Accordngly, under the assumpton that equlbrum n the chromatographc system s vewed as the dstrbuton of the analyte between two homogeneous and mmscble phases, one beng the moble phase and the other a lqud smlar to octadecane, the left-hand sde term n eq 9 should reman close to a constant over the temperature range nvestgated. Ths constant can be easly estmated from the characterstcs of the column (surface coverage, specfc surface area of the slca, mass of slca nsde the column, vod volume) and the molar volume of the lqud phases used. In the present case, the mass of slca n the column s 1.12 g, the specfc surface of the neat slca s 349 m 2 /g, and the surface coverage of the slca n C 18 chans s 3.85 µmol/m 2. Then N S 1.50 mmol. The vod volume of the column s 1.53 cm 3, and the molar volumes of the lqud mxtures CH 3 OH/H 2 O and CH 3 CN/H 2 O at 298 K are 20.4 and 22.8 cm 3 / mol. Then, at most, N M 75 mmol. The expected value of φ s then Fgure 1 shows plots of the left-hand sde term of eq 9 versus the temperature. The expermental retenton factors k were derved from the ntal slope (Henry s constant H) of the measured adsorpton sotherm (secton on Interpretaton of the Adsorpton Isotherm Data) and the column phase rato F. The actvty coeffcents were calculated accordng to the UNIFAC group method. 22 Although the agreement wth the expermental results s not as good as one mght wsh, the man advantage of usng the UNIFAC method s ts wde range of applcaton for vapor-lqud equlbra of nonelectrolytes mxtures. The typcal dfference between expermental and calculated values s 10%. The plots n Fgure 1A and B are a test of the valdty of the hypothess of a dstrbuton of the analyte between two mmscble lquds as a possble nterpretaton of the retenton mechansm n RPLC. The results showed that such a model completely fals for two reasons: (1) the plot exhbts an obvous decreasng trend whle the model predcts a constant or a slghtly ncreasng trend, and (2) the functons vary between 1 and 25 whle the model predcts a value 2-3 orders of magntude smaller (0.02). The lnear model of retenton appears to be too smplstc for the man reason that the adsorbed molecules of analyte may not Fgure 1. Plot of (γ M, /γ S, )k versus the temperature T. The actvty coeffcents were calculated acordng to the UNIFAC group method. Analyte phenol; Sunfre-C 18 column wth mxtures of (A) methanol and water (20:80, v/v) and (B) acetontrle and water (15:85, v/v) as the moble phase. Note the nconsstency of the expermental plots wth the thermodynamc model gven by eq 9. be completely embedded wthn the octadecane phase. These molecules have not necessarly access to the whole volume V S of the statonary phase. The analyte may also be smply adsorbed at the nterface between the layer of octadecane chans and the moble phase. In the next secton, we wll consder a more complex retenton model, n whch the analyte can be retaned by nteractons wth two dstnct statonary phases. (b) Case of a Heterogeneous Statonary Phase. Let assume now that the sample compound s dstrbuted not between two but between three homogeneous lquds. One of them s the same moble phase. Any possble source of moble-phase heterogenety wll be gnored. However, there are now two dstnct statonary phases, j, that act ndependently but are smultaneously n equlbrum wth the moble phase. Let V S,1 and V S,2 be the volumes of the statonary phases 1 and 2, respectvely. Consder that statonary phase 1 s smlar to pure octadecane (meanng that the compound molecule becomes embedded n the statonary phase) and statonary phase 2 s a hypothetcal mxture 4646 Analytcal Chemstry, Vol. 78, No. 13, July 1, 2006

6 Fgure 2. Expermental adsorpton sotherms of phenol measured by FA on Sunfre-C 18 wth a mxture of methanol and water (20:80, v/v) as the moble phase at sx dfferent temperatures. Note the mportant decrease of the saturaton capacty of the column at hgh temperatures. Fgure 3. Same as n Fgure 2, except the moble phase s a mxture of acetontrle and water (15:85, v/v) and the temperatures (fve temperatures only). Note the S shape of the adsorpton sotherms, especally vsble at room temperature. of the octadecane termnal methyl groups and methanol (representng the envronment of the analyte molecules adsorbed at the free ends of the bonded alkyl chans, n the adsorbed layer of methanol). The stoechometry of the mxture methyl groupsmethanol s assumed to be 1:1. The two equlbra are wrtten ( x S,1 x M)eq., ) γ M, S,1, γ The retenton factor becomes k ) V S,1 C S,1 S,2 + V S,2 C M V M C and ) F 1( C S,1 C M)eq, ( x S,2 x M)eq, ) γ M, S,2, γ (10) + F 2( C S,2 ) C M)eq, F 1 H 1 + F 2 H 2 (11) Introducng the molar fractons nstead of the molar concentratons and usng eq 10, eq 11 becomes k ) N S,1 N M M, γ γ + N S,2 S,1, M, γ N M γ S,2, (12) where N S,1 and N S,2 are the number of moles of statonary-phase molecules n the phases 1 and 2, respectvely. In eq 12, the actvty coeffcents are fxed and can be easly estmated by applyng the UNIFAC method to each one of the three phases at the dfferent temperatures consdered. The number of moles of solvent n the lqud phase (an aqueous soluton of methanol or acetontrle) was calculated as mentonned ( 75 mmol). k was measured expermentally. To ft the expermental data to eq 12, we assumed that the quanttes N S,1 and N S,2 are unknown but reman constant, ndependently of the temperature. Ths ft was unsuccessful, the fttng procedure endng up wth the best estmate for one parameter beng devod of any physcal sgnfcance (N S,1 < 0) and a poor regresson coeffcent (R ) 0.80). Analytcal Chemstry, Vol. 78, No. 13, July 1,

7 Table 2. Isotherm Parameters of Phenol on the Sunfre-C18 Column at Dfferent Temperatures wth a Mxture of Methanol and Water (20:80, v/v) as the Lqud Phase T (K) q S,1 (mol/l) 3.88 (3.92) a 2.02 (2.02) 1.63 (1.62) 1.40 (1.39) 1.21 (1.17) 1.11 (1.28) b 1 (L/moL) (0.337) (0.750) 1.08 (1.03) 1.29 (1.28) 1.46 (1.33) 1.62 (1.92) q S,2 (mol/l) 0.95 (0.95) 0.81 (0.81) 0.69 (0.71) 0.62 (0.63) 0.58 (0.64) 0.50 (0.30) b 2 (L/moL) 14.0 (14.5) 12.5 (12.4) 11.4 (11.1) 9.42 (9.38) 7.53 (7.21) 5.98 (7.74) q S,3 (mmol/l) 14.3 (4.4) 0.29 (0.43) 0 (0.06) 0 (0) 0 (0) 0 (0) b 3 (L/mmoL) (0.281) 2.44 (1.14) / (?) / (/) / (/) / (/) Henry s constant 16.2 (16.3) 12.4 (12.1) 9.63 (9.55) 7.65 (7.69) 6.13 (6.17) 4.79 (4.78) k a The values n parenthess are derved from the AED calculaton. The retenton model of lnear chromatography that s expressed by eq 12 mght make better physcal sense than the one gven by eq 9, but t stll does not ft properly to the expermental data. Ths means that a smple partton model between two or more phases s unrealstc. Ths challenges the actual meanng of the Van't Hoff plot, whch s abundantly appled n lqud chromatography and whch assumes a partton equlbrum between two phases characterzed by a molar enthalpy and a molar entropy of transfer, H and S, between the two standard states. Despte the fact that lnear Van't Hoff plots are often encountered n RPLC, ths does not mply that they should necessarly be accounted for a partton mechansm between a polar moble lqud phase and a hydrophobc statonary lqud phase. The results reported n ths secton show that the retenton mechansm n RPLC s far more complex than usually beleved. Ths orgnates from the complexty of the structure of the alkyl bonded statonary phase used and from the nature of the nterface of RPLC systems. Any sgnfcant varaton of the temperature, the moble-phase composton, and the pressure affects, sometmes drastcally, the retenton mechansm. The effects of these varatons cannot be accounted for based on mere thermodynamcs consderatons regardng the dstrbuton of the analyte between the moble and the statonary phases. One way to shed lght on the retenton mechansms n RPLC s to accumulate a set of adsorpton data and to study emprcally the evoluton of the adsorpton sotherm parameters (q S and b) wth, for example, the temperature, as done n ths work. The advantage of ths strategy s that no assumpton s made and the expermental results are clear, sound, and precse. The acquston of retenton factors k n a temperature range s nsuffcent to reveal the adsorpton propertes of an analyte n RPLC. Lnear chromatography does not provde enough nformaton on the heterogenety of adsorbent surfaces nor does t afford straghtforward conclusons regardng the temperature dependence of the thermodynamc propertes of adsorpton. Another lmtaton of lnear chromatography that s encountered even when a truly homogeneous adsorbent s used s that ths method does not dstngush between the contrbutons to the retenton factor of the saturaton capacty, q S, (or amount of an analyte formng a monolayer on the surface) and the adsorpton-desorpton equlbrum constant b.inthe case of an homogeneous surface (Langmur adsorpton sotherm) we can wrte k ) FH ) Fq S b (13) and, more generally, for an heterogeneous surface (case of N-Langmur adsorpton sotherms) k ) F (q S, b ) (14) )1 More expermental data are then needed to provde convncng evdence regardng the degree of heterogenety of adsorbent surfaces. By measurng retenton data n a wde concentraton range, we can assess the number of the types of adsorpton stes present on the surface, derve ther equlbrum constants, and ther contrbutons to the Henry s constant, H ) q S, b. Interpretaton of the Adsorpton Isotherm Data. The adsorpton sotherms of phenol were measured under the same expermental condtons as those used n lnear chromatography. They were measured for phenol concentratons between 0 and 160 g/l and between 0 and 35 g/l wth methanol and acetontrle, respectvely (the solublty s much lower n acetontrle than n methanol). Fgures 2 and 3 show the results. The sotherm data n water-methanol were ftted to a tr-langmur sotherm model, a model consstent wth the shape of the sotherm data and wth the adsorpton energy dstrbuton derved from the sotherm data. Fgure 3 shows that, wth acetontrle, the sotherm s S-shaped (convex upward at low and downward at hgh concentratons). The data were modeled wth a BET-Langmur sotherm. Ths result was reported earler, wth other C 18 -bonded columns. 13 The Langmur term accounts for adsorpton of the compound on the hgh-energy stes wthn the C 18 -bonded layer, the BET term for the accumulaton of the analyte n the multlayer of acetontrle (3-5 monolayers thck 13 ) at the top of the C 18 -bonded chans. (a) Adsorpton of Phenol from Methanol-Water (20:80, v/v). The best tr-langmur sotherm parameters are lsted n Table 2. These values are compared to those derved from the AEDs, shown n Fgure 4. A most nterestng result of the AED calculatons s to show that there are three types of adsorpton stes at ambent temperature but only two at hgh temperatures. Ths s confrmed by the results of the regresson analyss of the sotherm data. It becomes mpossble to calculate a set of parameters for a tr-langmur sotherm model at temperatures )N 4648 Analytcal Chemstry, Vol. 78, No. 13, July 1, 2006

8 beyond 311 K. Ths suggests that access to adsorpton stes deep wthn the bonded layer s affected by the temperature. The stes of type 3 are no longer accessble or dsappear (may be morphng nto type 2 stes?) when the moblty of the C 18 chans ncreases. The evolutons of the sotherm parameters (q S,1, q S,2, b 1, b 2 ) wth ncreasng temperature are shown n Fgure 5. Fgure 6 compares the contrbutons of each type of stes to the overall Henry s constant of phenol. It s clear that the varaton of the retenton of phenol wth temperature s controlled by ts adsorpton on the stes of type 2. The contrbuton of the stes of type 1 to the retenton of phenol s almost ndependent of the temperature. Most nterestng are the dfferences between the behavor of the stes of types 1 and 2. The saturaton capacty q S,1 decreases by a factor of nearly 3.5 whle the adsorpton-desorpton constant b 1 ncreases by a factor of 4.5 when the temperature ncreases from 295 to 351 K. It s unusual to observe an equlbrum constant that ncreases wth ncreasng temperature. Actually, the classcal equaton ln b ) ln b 0 + ɛ a, RT (15) Fgure 4. AED showng the logarthm of the adsorpton-desorpton constant of phenol (moble phase, methanol-water, 20:80, v/v) on Sunfre-C 18 versus the number of stes. The results are shown for the sx temperatures gven n Fgure 2. The rght-sde graphs are enlargements of the left-sde ones that llustrate the exstence of hghenergy stes wth very low saturaton capactes q S,. Note the decrease of the column heterogenety as well as the decrease of the dfference between the adsorpton energes on stes 1 and 2 (RT ln(b 2/b 1)) wth ncreasng temperature. that descrbes the dependence of ths constant on the temperature 24 no longer apples because the adsorpton energy ɛ a,1 s not constant over the temperature range nvestgated. Ths may be due to the moblty and the organzaton of the extremtes of the C 18 chans at the nterface wth the bulk moble phase ncreasng wth ncreasng temperature. It s lkely that ths provdes an ncreasng surface area of contact for adsorbate molecules. As for the stes of type 2, ther saturaton capacty decreases by a factor of nearly 2 and ther adsorpton-desorpton constant by a factor of 2.5 n the same temperature range ( K). Ths explans why these stes control the temperature dependence of the retenton of phenol, not the stes of type 1. Because the stes of type 2 are probably bured wthn the hydrophobc layer, ther surface area of contact wth the adsorbate and ther adsorpton energy does not vary much wth temperature. Equaton 15 apples well to these stes and the adsorpton energy derved from t, ɛ a,2, s 12.6 kj/mol, a value typcal of those that we have found wth several other columns for ths type of adsorpton stes. 7,11,12 However, we must keep n mnd that the preexponental factor, b 0, whch descrbes the molecular partton functon for the nternal degrees of freedom of solated adsorbate and solute molecules, s assumed to be temperature ndependent. It s noteworthy that the hgher the temperature, the more homogeneous the Sunfre-C 18 adsorbent. Ths effect results from the smultaneous decreases of the number of types of adsorpton stes (whch drops from 3 to 2) and of the dfference between the adsorpton energes of the stes of types 2 and 1 (whch drops from 9.1 to 3.8 kj/mol). Ths result agrees wth the AED plots shown n Fgure 4, n whch the dstance between the correspondng two modes dmnshes wth ncreasng temperature. However, the two modes are always well resolved, and even at 351 K, the two dstnct adsorpton modes are clearly observed. Fnally, the total saturaton capacty of the Sunfre column decreases by a factor 3 n the temperature range studed, (24) Jaronec, M.; Madey, R. Physcal Adsorpton on Heterogeneous Solds; Elsever: Amsterdam, The Netherlands, Analytcal Chemstry, Vol. 78, No. 13, July 1,

9 Fgure 5. Varaton wth temperature of the sotherm parameters. Stes 1 and 2 relate to the adsorpton of phenol on Sunfre-C 18. Moble phase: methanol-water mxture (20:80, v/v). (Top) Equlbrum constants. (Bottom) Saturaton capactes. Table 3. Isotherm Parameters of Phenol on the Sunfre-C 18 Column at Dfferent Temperatures wth a Mxture of Acetontrle and Water (15:85, v/v) as the Lqud Phase T (K) q S,1 (mol/l) b S,1 (L/moL) b L,1 (mol/l) q S,2 (mol/l) b 2 (L/moL) Henry s constant k Fgure 6. Contrbutons to the overall Henry s constant of phenol based on the ft of the adsorpton data (e.g., H ) q S,b ) versus the temperature. confrmng the result observed prevously wth a Symmetry-C 18 column. 15 Ths s an mportant result for preparatve chromatography, a feld of applcaton n whch a hgh column capacty s useful. Although a hgh column temperature would not be helpful from ths vewpont, the negatve effect of a loss n saturaton capacty s compensated by a decrease n the degree of heterogenety of the column and a marked ncrease n the solublty of the feed components n the moble phase. (b) Adsorpton of Phenol from Acetontrle-Water (15: 85, v/v). The adsorpton sotherm data of phenol from the aqueous soluton of acetontrle are shown n Fgure 3 at fve dfferent temperatures. The best BET-Langmur sotherm parameters are lsted n Table 3. These sotherms are ntally convex downward, exhbtng ths tell-tale sgn of sgnfcant adsorbateadsorbate nteractons. Thus, t was not possble to calculate the 4650 Analytcal Chemstry, Vol. 78, No. 13, July 1, 2006

10 Fgure 7. Same as n Fgure 5, except the moble phase, a mxture of acetontrle and water (15:85, v/v). The descrpton of each parameter of the BET-Langmur sotherm s gven n the text. AEDs n ths case snce the EM program assumes local Langmur sotherm. Any sum of Langmur sotherms cannot generate an S-shaped sotherm smlar to those observed n Fgure 3. As a result, the followng conclusons are based on the sole regresson analyss of the adsorpton data, wthout ndependent confrmaton. It was prevously shown 13 that acetontrle forms an adsorbed multlayer system on C 18 -bonded phases. Solutes such as phenol can dssolve and accumulate as a multlayer system formng a second statonary phase. Acetontrle cannot nteract strongly wth the hydroxyl group of phenol through hydrogen-bondng Analytcal Chemstry, Vol. 78, No. 13, July 1,

11 Fgure 8. Same as n Fgure 6, except the moble phase, a mxture of acetontrle and water (15:85, v/v). nteractons, lke methanol does. As a result, phenol-phenol hydrogen-bondng nteractons take place n the acetontrle layer, allowng the formaton of an adsorbed multlayer of phenol molecules on the surface of the C 18 adsorbent. The monolayer saturaton capacty on the stes of type 1 s barely affected by the temperature, and n contrast wth the methanol case, the adsorpton-desorpton constant of phenol on the surface of the C 18 -bonded layer decreases contnuously wth ncreasng temperature (Fgure 7). However, the plot of ln b S,1 versus 1/T s not lnear and eq 15 does not apply. It seems that the adsorpton energy s larger at hgh than at low temperatures. On the other hand, the adsorpton-desorpton constant of phenol on a monolayer of adsorbate molecules follows eq 3. Note that ths plot s lnear f both the adsorpton energy and the factor b 0 are consdered to be temperature ndependent, whch s theoretcally ncorrect. 24 The slope of ths plot would gve an adsorpton energy of 22.7 kj/mol, a value that s surprsngly large. Fgure 3 clearly shows that the concentraton of the nflecton pont of the sotherm ncreases wth ncreasng temperature. The sotherm tends progressvely to become Langmuran (n ths case, t tends toward a b-langmur sotherm), and the role played by the adsorpton stes of type 2 becomes more mportant. The saturaton capacty q S,2 ncreases sgnfcantly wth ncreasng temperature whle the adsorpton-desorpton constant b 2 decreases. Fgure 8 shows the varatons of the Henry s constant of phenol wth ncreasng temperature. Note how the role played by the stes of types 1 and 2 s dfferent whether methanol or acetontrle s used as the organc modfer. Although the overall retenton factor decreases wth ncreasng temperature n both cases, the contrbuton of the stes of type 1 decreases and that of the stes of type 2 ncreases when acetontrle replaces methanol. Comparson between the Results of Lnear and Nonlnear Chromatography. The results derved from lnear chromatography and the Van't Hoff equaton would suggest that phenol does partton between the moble phase and a homogeneous lqud statonary phase. Its equlbrum between these two phases as a smple lqud-lqud equlbrum and the assocated varatons of the enthalpy and the entropy would correspond to the transfer of 1 mol of phenol between the two mmscble phases, the polar moble phase and the octadecyl layer. As demonstrated n earler, t s unrealstc, however, to consder the surface of a C 18 bonded porous slca adsorbent as a homogeneous statonary phase, akn to lqud octadecane, for example. The octadecyl chans are not free but bonded to the slca surface, whch reduces consderably ther moblty and modfes drastcally ther organzaton and structure. Furthermore, the complex nature of the C 18 bonded layer makes possble for the analyte molecules to adsorb onto some patches of exposed bare slca or to bury themselves n the bonded layer, as well as to adsorb at the nterface between these alkyl chans and the moble phase. These facts render mplausble the assumptons underlyng the Van't Hoff equaton. In contrast, the results of the measurements carred out at hgh concentratons demonstrate the complexty of the equlbrum sotherm. Ths complexty can be explaned only by the heterogenety of the surface of the C 18 -bonded adsorbent used. The complexty of the temperature dependence of the parameters of the equlbrum sotherm suggests that each one of the retenton equlbra dentfed earler s not as smple as the analogy wth the adsorpton at the planar nterface between a conventonal sold adsorbent and a lqud would suggest. The envronment of the adsorbate vares from place to place on the surface, and dependng on the solute consdered and the brand of RPLC adsorbent nvestgated, up to four dfferent types of adsorpton stes have been found, wth adsorpton energes rangng from a few to more than 20 kj/mol. 6 Also, the envronment of a gven ste seems to depend on the temperature. So, the number of adsorpton stes of each type seems to depend on the temperature, the stes of certan types morphng nto those of another one, due to the reorganzaton of the bonded C 18 chans. In the process, the adsorpton energy on the stes of certan types also changes and the effect s dfferent for the dfferent stes. These effects are llustrated n Fgures 6 and 8 that show plots versus the temperature of the contrbutons of the two dfferent types of stes dentfed for phenol on Sunfre to the Henry constant. These results are not surprsng. The number of adsorpton stes and the envronment between the C 18 chans, hence the nteractons between solute molecules and C 18 chans, change contnuously wth ncreasng temperature. It s mpossble to assume that the nature and densty of the dfferent patches reman constant when the temperature vares. What s surprsng s that the values measured for the overall retenton factor ft so well to the van t Hoff equaton. CONCLUSION Ths work demonstrates that the problem of dervng thermodynamc parameters related to the transfer of the solute between the lqud and the statonary phase n RPLC has no satsfactory soluton. The C 18 -bonded layer cannot be consdered as a conventonal adsorbent, defned as a thermodynamc phase. The adsorpton behavor of low-molecular-weght compounds s too complex, the adsorbent surface s heterogeneous, the structure of the hydrophobc layer s very flexble, and the arrangement of the C 18 chans change wth the temperature, so retenton factors cannot be related to a sngle dstrbuton constant K between the moble and the statonary phases. Thus, the classcal C 18 -bonded phase cannot be consdered as equvalent to ether lqud octadecane or a smple sold surface and retenton n RPLC cannot be accounted for by one dstrbuton factor between octadecane and the aqueous soluton of an organc modfer. As a result, t seems that the lnear or quas-lnear behavor of the Van't Hoff plot, whch s generally observed, should be 4652 Analytcal Chemstry, Vol. 78, No. 13, July 1, 2006

12 consdered as accdental. The overall retenton factor of solutes measured n lnear chromatography s actually the sum of the contrbutons of dfferent retenton mechansms,.e., of adsorpton on dfferent types of stes. Whle retenton ncreases on one type of stes wth ncreasng temperature, t decreases more strongly on another type of stes and the compensaton between these two effects results n the overall retenton factor decreasng wth ncreasng temperature, n agreement wth Van't Hoff law (or at least approxmately so; see Fgure 1). The complexty of RPLC adsorpton s further llustrated by the large dfference between the temperature effects on the adsorpton behavor of phenol that s observed n aqueous solutons of methanol or acetontrle. Wth methanol, the contrbutons of the low- and the hgh-energy stes to the overall retenton ncrease and decrease, respectvely, wth ncreasng temperature. The converse s observed wth acetontrle. Ths suggests that the temperature effect on the moblty and structure of the C 18 chans s dfferent n methanol and n acetontrle. It was already known that these two solvents adsorb very dfferently on C 18 -bonded slcas. Our results show that these dfferences affect the structure of the bonded hydrophobc layer, ts dynamc, and the accessblty of the adsorpton stes by the analyte molecules. Ths work also rases questons on the precson and the accuracy of the adsorpton data measured by FA and on ther nterpretaton. The accuracy of FA s well establshed. We measured and appled the necessary correctons (.e., for the contrbuton of the extracolumn volume). The precson of the measurements has been establshed earler. It s confrmed by the hgh degree of self-consstency of the data (see Fgures 2 and 3). The modelng of the data leaves a small sum of resduals. Obvously, the precson of the parameters of the two Langmur stes s less than that of the data, but the valdty of the sotherms s confrmed by the agreement (not shown) between the calculated and expermental hgh-concentraton band profles. The nterpretaton of the results by the complex structure of the nterface between the bulk lqud phase and the RPLC adsorbent and ts hgh senstvty to changes n the temperature or the moble-phase composton s hghly plausble. Yet, t mght also be based on an ncorrect extrapolaton of an approach that was shown to predct accurately the overloaded band profles 2. Thus, ndependent verfcatons of the valdty of our method and of the present results must be obtaned. We plan to apply FA and model adsorpton data obtaned for more classcal sold-lqud systems for whch a sold surface s drectly n contact wth the lqud phase, wthout the fuzzy layer of the bonded alkyl chans. Fnally, our results show that ncreasng the column temperature tends to render the surface of C 18 -bonded slcas more homogeneous. The dfference between the adsorpton energes on the stes of types 1 and 2 (those that have the lowest two adsorpton energy) decreases sgnfcantly wth ncreasng temperature. Thus, ncreasng the column temperature mproves the column effcency by acceleratng mass transfers and also by reducng the degree of peak talng. Ths concluson s consstent wth recent results obtaned by NMR spectroscopy, whch have shown the same effect of the temperature on the conformaton and moblty of the bonded alkyl chans. 25,26 ACKNOWLEDGMENT Ths work was supported n part by grant CHE of the Natonal Scence Foundaton and by the cooperatve agreement between the Unversty of Tennessee and the Oak Rdge Natonal Laboratory. We thank Uwe Neue and Maranna Kele (Waters, Mlford, MA) for the generous gft of the Sunfre- C 18 column used n ths work and for frutful and creatve dscussons. Receved for revew January 30, Accepted Aprl 10, AC (25) Srnvasan, G.; Kyrlds, A.; McNeff, C.; Müller, K. J. Chromatogr., A 2005, 1081, 132. (26) Pursch, M.; Sander, L. C.; Albert, K. Anal. Chem. 1999, 71, 733A. Analytcal Chemstry, Vol. 78, No. 13, July 1,