A d . Chem. 1994,66,139-146
Solvation Parameter Model tor the Prediction of Breakthrough Volumes in Solid-Phase Extraction with Particle-Loaded Membranes Mary t. Lrrrtvw and cofkr F. Pode' Department of Chemlstty, Wayne State Universfty, Detroit, Mchigan 48202 The experimental factors which establish the breakthrough volume in solid-phase extraction are interpreted using a theoretical model proposed by Lovkvist and Jonoson. For Wthmugb vohunesdeterminedover a m w mkge of ample hrates, in which the sorption capacity of tbe sorbent is not exceeded, it is shown that the dominant parameter in determining the breakthrough volume is the retention of the analyte in tbe sampling system. This enables a predictite model to be proposed for the estimation of breakthrough volumes for a large number of analytes using eitber sohation or sohatochromic parameters to characterize analyte retention. Tlje success of this approach is denmustrated by tbe excellent agreement between the calculated and experimental breakthrough volumes obtained for about 25 varied anrlytes on particle-loadedmembranes containing octadecylsized silica particles ( r > 0.99 and standard error in the estimate of 0.07 log unit). The model clearly demonstrates that the most important parameter in determining the breakthrough volume of an analyte in an aqueous solution is its molecular volume and that polar interactions such as orientation and hydrogenbondrcid/base interactions are unfavorablefor retention. The relative contributiom of intermolecular interactions to tbe breakthreugbvolup~eare quantitatively identified by the model which providesamechPaiomforthe ratiddesignof a sampling system to meet the needs of differeat analytes. Solid-phase extraction cartridges were introduced in the late 1970sas a replacement for liquid/liquid extraction sample preparation procedures for either matrix simplificationor trace enrichment of organic analytes.ld Liquid/liquid extraction procedures were viewed as being labor intensive, comparatively difficult to automate, and requiring the use of relatively large volumesof high-punty solvents that wereexpensive to purchase and, in some cases, equally as expensive to dispose of in an environmentally acceptable manner. Albeit with some compromises, solid-phase extraction has fulfilled its early promise and is now a widely used aad acceptable technique in many analytical laboratories. The general acceptance of solid-phase extraction is based on its proven ability to provide acceptable performance in a number of sample preparation procedures (1) Poolc, C. F.; Poole, S. K. Chromatography Today; Elscvicr: Amsterdam,
with considerable cost savings and convenience. It is also recognized, however, that solid-phase extraction cartridges are 'not without attendant problems which can be briefly summarized as follows: the small cross-sectional area of cartridges results in slow sample processing rates and a low tolerance to blocking by particulates and adsorbed matrix components; channeling reduces the capacity of the cartridge bed to retain analytes (decreases the breakthrough volume); the reproducibility of sorbents from lot to lot and between manufacturers leaves a lot to be desired; incomplete reversibility of the sorption 6f some analytes from active sorbent sites; and contamination of the isolated sample fraction by imparities originating from the manufacturing and packaging process,1.4.7-10 The basic design of solid-phase extraction cartridges has changed little since their inception. A typical solid-phase extraction cartridge consists of a small column (generally an open syringe barrel) containing an irregularly shaped chemically bonded silica sorbent with i n average particle size of 40 pm packed between porous metal or plastic frits. The most common configuration contains about 100-500 mg of chemically bonded silica packing, although other sizes and packing materials are available. New products for solid-phase extraction have appeared in the last few years which could be considered a rethinking or further evolution of the solid-phase extraction concept. Specifically,particle-loaded membranes have been introduced which provide shorter sample processing times due to their higher flow rates (large cross-sectional area and decreased pressure drop), decreased plugging by particulates (large crosssectional area) and improved mass-transfer characteristics, and reduced channeling (particles with a smaller average particle diameter and improved mechanical stability of the sorbent bed).'l,l2 The particle-loaded membranes in the form of flexible disks of various diameters and 0.5" thickness consist of sorbent particles of about 8-pm diameter (90%w/w) immobilized in a web of poly(tetrafluoroethy1ene)microfibrils. For general use the membranes are supported on a fritted glass filter in a standard filtration apparatus, using vacuum to generate the desired flow of sample through the membrane. They have been used successfully for environmental analysis
1991.
( 2 ) Pool& S. K.; Dean, T.A.; Oudrema, J. W.; Pook, C. F. AMI. Chim. Acfa 1990. 236, 3-42. (3) Namianik, J.; Gomti,T.; BiPiuL. M.AMI. Chim. Acta 1990, 237, 1-60, (4) Lirka, 1.; Krupdt J.; Lcclcrcq P. A. J . High Rcsolur. Chromarogt. 1989,12. 577-590. ( 5 ) Barctlo, D.A @ ~ w 1991, 116, 681. (6) Horack, J.; Majora, R. E. LC-GC 1993. 11, 74-90. ooO3-2700/94/03660139504.50/0 0 1993 Ammican chsmlcel Soclety
(7) Muto, V.; Soltts, L.; Radova, K. 1. Chromatogt. Sci. 1990, 28, 403406. (8) Moors, M.; Massart, D.L. AMI. Chim. Acta 1992, 262, 135-144. ( 9 ) Wells, M. J. M.; Michael, J. L.1. Chromafogr.Sci. 1987, 23. 345-350. (10) Hennion, H. C. Tnndc AMI. Chem. 1991, IO, 317-323. (11) Hagen, D. F.; Markell, C. G.; Schmitt, G.; Blevins, D. B. AMI. Chim. Acta 1990, 236, 157-164. (12) Markell, C.; Hagen, D. F.; Bunnelle, V. A. LC-GC 1991, 9, 332-337.
Ana!YikalGhmWry, Vd. 66, No. 1, Jenuery 1, 1994
tM
(particularly trace organic compounds in water) lI-16 and in clinical ana1y~is.l~Similar materials in the form of larger sheets are available as stationary phases for thin-layer chromatography,l”mand their characteristickineticproperties have been established by forced flow thin-layer chromadevelopmemt was the introduction t o g r a p h ~ . ~ ]A- ~further ~ of glass microfiber disks impregnated with chemically bonded silica particles.25 The microfiber disks are rigid, eliminating the necessity for an external support, and use only a fraction of the bed mass employed in conventional solid-phase extraction cartridges (1.5-30.0 mg). The low bed mass is important since it minimizes the volume of solvents consumed in conditioning the disk and in recovery of analytes from the disk. The small bed mass also reduces interferences from weakly retained nonspecific matrix components, leading to cleaner extracts. Particle-impregnated porous poly(viny1 chloride) disks have been developed for improved isolation of biopolymersand for preparative liquid chromatography when stacked in series (stacked-membrane chromatography).26 Supported liquid impregnated porous poly(tetrafluoroethy1ene) membranes have been used in flow sample processing to selectively isolate analytes from a donor stream (sample) with transfer to an acceptor stream for recovery.27 Thus, at the moment, various approaches to sample preparation involving membrane (or disk) technology are under active development, and it is likely that these techniques will become increasingly important as knowledge builds concerning their optimum design and the number of validated analytical methods employing this new technology increases. The effectiveness of a solid-phase extraction device for isolating an analyte from a sample can be described in terms of its capacity, kinetic properties, and retention. Taken together, these three parameters establish the breakthrough volume for the analyte in the sampling system. A working definition of the breakthrough volume can be stated as the volume of sample, assumed to have a constant concentration, that can be passed through the solid-phase extraction device before the concentration of the analyte at the outlet of the device reaches a certain fraction of the concentration of the analyte at the inlet. The ratio of the inlet to outlet concentration is arbitrarily defined by different authors in accordance with how the outlet concentration is to be e s t a b l i ~ h e d . ~ , The ~ * ~capacity ~ - ~ ~ of a solid-phase extraction (13) Kraut-Vaas, A.; Thoma. J. J. Chromarogr. 1991,538, 233-240. (14) Evans. 0.;Jacobs, B. J.; Cohea, A. L. Analysr 1991, 116, 15-18. (15) Brouwer, E. R.; Lingeman, H.; Brinkman, U. A. Th.Chromatographia1990, 29,415-418. (16) McDonncll, T.; Roscnfeld, J.; RaiiFirouz, A. J. Chromatogr. 1993,629,4153. (17) Lensmcycr, G. L.; Wiebc, D. A.; Darccy, B. A. J. Chromatogr.Sci. 1991,29, 444-449. (18) Poolc, S.K.; Poolc. C. F. J. PIanar Chromatogr. 1989. 2, 478-481.
(19) Poolc, S.K.; Fcmando, W. P. N.; Poole, C. F. J. Planar Chromatogr. 1990, 3, 331-335. (20) Issaq, H. J.; Sebum, K. E.; Hightowcr, J. R. J. Uq. Chromatogr. 1991, 14,
1511-1517. (21) Botz, L.; Nyiredy, Se;Wehrli, E.; Stichcr, 0.J. Uq. Chromatogr. 1998,13. 2809-2828. Fernando, W. P. N.; Poolc, C. F. J. Planar Chromarogr. 1990, 3, 389-395. (22) Fernando, W. P. N.; Poole, C. F. J . Planar Chromatogr. 1991, 4, 278-286. (23) Fcmando, W. P. N.; Poolc, C. F. J. Planar Chromatogr. 1992.5, 50-56. (24) Fernando, W. P. N.; Larrivee, M. L.; Poole, C. F. Anal. Chem. 1993, 65, 588-595. (25) Hearnc, G. M.; Hall, D. 0. Am. Lab. 1993, 28H-28M. (26) Frey, D. D.; Van de Water, R.; Zhang, B. J. Chromarogr. 1992.603.43-47. (27) Jonpson, J. A,; Mathiason. L. Trends AMI. Chem. 1992, 11, 106-114. (28) Joscfson, C. M.; Johnston J. B.; T ~ b c yR. , AMI. Chem. 1984,56,764-768.
140 Amljlficel chemistry. Vd. 66, No. 1, Jenuery 1, 1994
device depends on the number of available sorption sites for the analyte and retained matrix components. Saturation of these sites leads to breakthrough because of a lack of retention or distortion of the sorption isotherm resulting in lower retention as the surface concentrationof sample on the sorbent surface increases. It is related to mass overload and will only become important when the concentration of analyte and/or sorbed matrix is high. Typical chemically bonded sorbents have a capacityof about 1-10% (w/w), and this limit isunlikely to be exceeded during trace enrichment of common samples such as surface waters, biological fluids, etc. Under average conditions the breakthrough volume is controlled by kinetic parameters and by retention. To understand how the breakthrough volume depends on these parameters, a suitable model is needed to describe the sorption process in terms of the relevant parameters. The sorption of an analyte by a solid-phase extraction device can be described by a frontalanalysismodel. The derivativeof the breakthrough curve in this model is similar to a Gaussian-shaped c u r ~ e . 2 ~ ~ ~ The breakthroughvolume, VB,can then be formally described by the function VR- 2uv (n > 4) or VR - 3uv (n > 9) where VRis the retention volume, uv the standard deviation, and n the number of theoreticalplates for the Gaussian-shapedcurve. The breakthrough volume can then be expressed by eqs 1 and 2, where 16 is the capacity factor for the analyte in the sample
vB = [(nl” - 2)/n1/21(1+ k , ) ~ , , ,
for n > 4
VB [l - (3/n1/’)](1 + k,)V,,, for n > 9
(1)
(2)
matrix as mobile phase and V m the holdup volume (dead volume) of the sorbent bed. For particle-loaded membranes of 0.5“ thickness eq 1 was shown to provide a poor fit to experimental data, and since n has values between 4 and 9 at typical flow rates, eq 2)is i n a p ~ l i c a b l e .Lovkist ~ ~ and Jonsson adopted a different numerical solution to the frontal analysis distribution of analytes on columns with low values of n and derived the relationship32 V, = ( C I ,
+ + $)-li2(l + k,)V,
(3)
where a, = (1 - b)2, a1 and a2 are complex functions of b evaluated from tabular data in ref 32, and b is the breakthrough level (the fraction of the total mass ofanalyte which has passed through the column). Within the limits of the data given in ref 24, Fernando et al. demonstrated that eq 3 provided a reasonable description of the breakthrough volumes for a number of analytes extracted from water by particle-loaded membranes. Considering eq 3, the breakthrough volume is directly proportional to the holdup volume for the sampling device. Given a homogeneous packing density increasing the size of the sampling device will increase the sample volume that can be processed before breakthrough. Increasing the size of the (29) Frei, R. W.; k h , K.Selective Sample Handling and Detection fn HighPerformance Uquid Chromurography. Part A; E l d e r : Amsterdam, 1988; pp 5-80. (30) Gocwic, C. E.; Hogcndoorn,E. A. Sei. Toral Emiron. 19885, 47, 349-360. (31) Mol, H. G. J.;Stanicwski, J.; Jansscn, H.-G.;Cramers,C. A.;Ghijsen,R.T.; Brinkman, U. A. Th. J. Chromurogr. 1993,630,201-212. (32) Lovkvist, P.; Jonsson, J. A. AMI. Chem. 1987,59,818-821.
T.#.
1. Influmw d Kh;rtlo Poromoton on tho brorkthrough Vokrm
flowrate
Im.of
them
(mL/mm)
plates
quotient ineq3
flowrate (mL/min)
5 10 13 20 30
6.5 8.4 9.0 8.5 7.7
0.535 0.592 0.608 0.596 0.573
40 60
80 100
no. of theor plates
quotient ineq3
0.6 5.9 4.2 3.6
0.539 0.485 0.430 0.405
sampling device, however, increases the volume of solvent that is required to desorb the extracted analytes as well as increasing the concentration of matrix components that are coextracted and subsequently reconcentrated along with the analytes of interest. Thus, in practice, V m is limited to a small range of values given the intended use of the device, and we can assume that V, is fixed by the design of the device for the present discussion. The influence of the kinetic performance of the sampling device on the breakthrough volume is contained in the first part of the left-hand side of eq 3. The homogeneity and quality of the sampling bed and the sample processingrate will influencethe breakthrough volume through the dependence of n on these parameters for any defined level of breakthrough. This contribution can be evaluated numerically for particle-loaded membranes from the data provided in ref 24 for a 47-mm-diameter disk (Table 1) and a breakthrough level of 1%. The data show that there is an optimum flow rate at which the breakthrough volume reaches a maximum at about 13 mL/min. The breakthrough volume is reduced at both very low and high flow rates. Between 10 and 30 mL/min the breakthrough volume is not strongly affected by the sample flow rate. If the breakthrough volume is to be standardized as an experimental parameter, it should be determined over a narrow range of flow rates to avoid significant variations between experiments. (Since n also depends on the diffusion coefficient of the analyte, tfie breakthrough volume is not independent of the diffusion coefficient. The diffusion coefficient in a constant sample matrix depends largely on the molecular weight, so that unless analytes of vastly different molecular weights are being considered, this affect will not be significant). With V, fixed and breakthrough measurements made over a narrow range of flow rates, eq 3 indicates that the dominant parameter that influencesthe breakthrough volumeof different analyteswithin the sampling system is retention, and therefore, it should be possible to predict breakthrough volumes with acceptable accuracy from a knowledge of the retention parameter, k,, in eq 3. The determination of k, directly for all compounds of interest, however, is not such a simple task. For particle-loaded membranes, somevalues of k,for a number of aromatic compounds were estimated from retention data obtained using forced-flowthin-layer chromatography.u This equipment is not readily available in most analytical laboratories and limits this approach. Presumably, equivalent data could be generated using liquid column chromatography if packing material identical to the sorbents used to prepare the particle-loaded membranes was available from which to prepare suitable columns. In either case, the capacity factor value representing the retention of the analytes of interest in the sample matrix (usually water containing 1% or so of organic solvent to ensure complete wettability of the membrane for
large samplevolumes) is determined indirectlyby extrapolation of retention data obtained at higher concentrations of organic solvent in water. The primary problem with this approach is the uncertainty in the value of k,,which cannot be identified from the model used for the extrapolation since deviations from the model equations at low concentrations of organic solvent, the region of most interest for the prediction of breakthrough volumes, vary significantly for different solutes.13-36 A preferable method would be one that enabled values of the breakthrough volume to be estimated directly from solute properties. Josefson et a1.28and Thurman et al.37 haveshown that the logarithm of the aqueous molar solubility was well correlated with the logarithmof the capacity factor for analytes isolated on macroporous polymeric resins. This method, although useful, ignores stationary-phase contributions to retention and is limited by the availability and quality of solubility data (particularly for sparingly soluble solutes). At this time, a very large number of solubility-relatedphenomena and transfer properties have been characterized using linear solvation energy relationships and a cavity model These models can be written in several forms. The two most pertinent expressions to this discussion are
SP = c + mV,/100 + ma*+ d6, SP = c
+ UCY, + b&,
(4)
+ mVx/lOO + rR, + STY + aay + b#
(5)
where SP is a free energy related solute property (in this case either the solute capacity factor or breakthrough volume), V is a parameter characteristic of the size of the solute, uzis a measure of the solute’s ability to stabilize a neighboring dipole by virtue of its capacity for orientation and induction interactions, Rz is the solute’s excess molar refraction, 62 is an empirical correction factor to allow for the solute’s own polarizability, and a and pare parameters characterizing the solute’s hydrogen-bond acidity and hydrogen-bond basicity, respectively. Equation 4 is cast in terms of the solvatochromic parameters with VIas the intrinsic molecular volume. The subscript m indicates the use of themonomer values for solutes that are capable of self-association. Equation 5 is cast in terms of the solvation parameter model of Abraham with VX as the characteristic molecular volume and the superscript H, indicating the use of solvation parameters derived from equilibrium measurements. The system constants c, m,r, d, s,a, and b are solute independent and are characteristic of the sampling system, stationary phase, and sample solvent. These parameters are evaluated by multiple linear regression by determining the property SP (in this particular case the logarithm of the breakthrough volume) for a series of solutes with known explanatory variables. Once established, the property SP can be estimated for any solute in the same (33) Hsieh, M.-M.; Dorscy, J. G. J. Chromorogr. 1993, 631, 63-78. (34) Chen, N.; Zhang, Y.; Lu, P. J . Chromotogr. 1992, 603, 35-42. (35) Chen. N.; Zhang, Y.;Lu, P. 1. Chromatogr. 1993, 633, 31-41. (36) Kaibara, A,; Hohda, C.; Hirata, N.; Hirose, M.; Nakagawa, T. Chromotogrophia 19w, 29, 275-288. (37) Thunnan, E. M.; Malcolm, R. L.; Aiken, 0. R. Anal. Chem.. 1978,50,775779. (38) Abraham, M. H. Chem. Soc. Rev. 1993.22, 73-83. (39) Poole, C. F.; Kollie, T.0.;Poolc. S . K. Chromurographiu 1992,34,281-302. (40) Kamlct, M. J. Prog. in Phys. Org. Chem. 1993, 19, 295-317. (41) Taft, R. W.;Abboud, J.-L. M.; Kamlct, M. J.: Abraham, M. H. 1.Solution Chem. 1985, 14, 153-186.
sampling system for which the solute explanatory variables are known or can be reasonably estimated from empirical combining rules. The multiple linear regression models represented by eqs 4 and 5 have &en used previously to predict the influence of solvent composition on retention in reversed-phase liquid chromatography.4248 This process is analogous to the prediction of breakthrough volumes employed in these studies, except that the solvent composition is fixed. It should be noted that the general evolution in model parameters has rendered some of these earlierstudiesin liquidchromatography less reliable in specific details but the general picture is still sound.
EXPERIMENTAL SECTION Organic solvents and water were Omnisolv grade from EM Science (Gibbstown, NJ). The Empore particle-loaded membranes in the form of 47-mm disks were obtained from J. T. Baker (Phillipsburg, NJ) and contained octadecylsilanized silica gel particles. Other chemicals were reagent grade or better and obtained from several sources. Experimental breakthrough volumes for the particle-loaded membranes were obtained using a standard vacuum filtration apparatus (Millipore Corp., Bedford, MA) connected to a water aspirator via a flow metering valve, as described by Hagen et al." The membranes, supported on a fritted glass disk, were washed with acetonitrile (10 mL) to remove contamination prior to use. The wash solvent was allowed to permeate the disk for a few minutes before pulling it through the membrane, which was then dried by pulling air through it for about 10 min. The disk was activated with methanol (IOmL), by allowingit topermeate thedisk for a few minutes, followed by aspirating the solvent through the membrane and releasing the vacuum before the last drop of methanol had passed through the membrane. The disk was then washed with water (10 mL) followed by application of the sample without allowing the disk to become dry. The samples were aspirated through the membrane at an accurate flow rate of 40 f 3 mL/min. After the sample had been processed, the receiver was changed for elution of the standards with 2 X 5 mL aliquots of acetonitrile. The first aliquot was allowed to permeate the disk for a few minutes before aspirating through the membrane, followed by the second aliquot of acetonitrile. Since some of the standards used in this study have significant vapor pressure, the drying time for the disk between processing the sample and elution of the standards should be minimized to avoid sample losses. The combined aliquots of acetonitrile were then transferred to a 10-mL vohmetric flask, a suitable internal standard was added, and the solution volume was adjusted to the mark. Each extraction was performed in triplicate. The recovery of the standards was determined by gas chromatography.
Standard solutionswere prepared in astonitrile and added to water containing 0.5% (v/v) methanol to give a known amount of standard, 1&20 pg, in a aqueous solutioncontaining a total of 1.O% (v/v) methanol and acetonitrile. Standards were processed in groups of three to five compounds per experiment to reduce the time required to acquire the data. Representativecompounds were also run in different mixtures to ensure that there were no significant interactions between compounds that affected the accuracy of the breakthrough volume measurements. Initially,sampleswere screened using decade changes in the sample volume to estimate the approximate breakthrough volumes, followed by a more systematic experimental design. For compounds with a breakthrough volume between 0 and 50 mL, measurements were made at 2.5-mL volume increments, 50 and 100 mL at 5-mL increments, 100 and 1000 mL at 10-mL increments, and greater than 1000 mL at 100 mL increments. The data were subsequently plotted as breakthrough curves and the breakthrough volumes estimated using the line providing the best fit through the data. The solvatochromic and solvation parameters for the standard compounds used in the multiple linear regression models, equations (4) and (3,are summarized in Table 2. The Kamlet-Taft solvatochromicparameters were taken from refs 40, 49-5 1. The characteristic molecular volumes were calculated using the incremental constants and method described by M c G ~ w a n . ~The ~ . ~excess ~ molar refraction, R2, was calculated from the solute's refractive index as described by Abraham et al.54 The other solvationparameters for Abraham's model were taken from refs 38 and 55-59. Multiple linear regression analysis was performed using the program SPSS V4.0 (SPSS, Chicago, IL) on an Epson Apex 200 personal computer.
RESULTS AND DISCUSSION The parameter that is most useful in characterizing the effectiveness of a solid-phase extraction device for isolation or concentration of a selected analyte is its breakthrough volume. Breakthrough volumes can be determined experimentally on a compound by compound basis, but this is a very time-consuming process and very few reliable values are available in the literature. Also, although it is clear that the breakthrough volume depends on the properties of a solute, it can only be defined within the system parameters employed for its determination. Therefore, it must be treated as a system parameter. Of the three parameters (capacity, kinetic characteristics, reteqtion) known to control the breakthrough
(49) Abboud, J.-L. M.;Roussel,C.;Gcntric,E.;Snidi,IC,LaurallJ.;Guiheneuf, llan, G.; Kamlet, M. J.; Taft, R. W. J. Org. Chem. 19%(1,53,1545-1550. (50) Kamlet, M.J.; Dohcrty, R. M.;A b r d m , M. H.; Taft, R. W. Quanr. Stact.-Act. Rela. 1988. 7, 71-78. (51) Kamlet, M.J.; Doherty, R. M.;Abraham, M. H.; Marcus,Y. Taft, R. W. J . Phys. Chem. 1!3SS, 92, 5244-5255. (42) SadeL,P.C.;Carr.P.W.;Dohcrty,R.M.;Kamlct.M.J.;Taft,R.W.;Abrahaa (52) McGowan, J. C. J. Appl. Chem. Blotechnol. 1978, 28. 599-607. M.H. AMI. Chem. 1985, 57,2971-2978. (53) Abraham, M. H.; McGowan, J. C. Chromatographh 1987, 23, 243-246. (43) Cam, P. W.; Doherty, R. M.; Kamlet, M.J.; Taft, R. W.; Melander, W.; (54) Abraham, M.H.; Whiting, 0. S.; Doherty, R. M.; Shucly. W. J. J. Chem. Horvath, C. AMI. Chem. 1986,58, 26744680. Sm., Perkin Trans. 2 1990, 1451-1459. (44)k h y , D. E.; Carr, P. W.; Pearleman. R. S.; Taft, R. W.; Kamlet. M.J. (55) Abraham,M.H.;Whiting,G.S.;Doherty,R.M.;Shulcy, W. J. J. Chromarogr. Chromalographla 1986, 21,473-477. 1991,587,213-228. (45) Kamlet, M.J.; Abraham, M.H.; Carr, P. W.; Doherty, R. M.;Taft, R. W. (56) Abraham,M.H.; Whiting,G.S.;Dohcrty,R. M.;Shucly,W. J. J. Chromarogr. J. Chem. Sm.. Perkin Trans. 2 1988,2087-2092. 1991,587, 229-236. (46) Park, J. H.; Cam, P. W.; Abraham, M.H.;Taft, R. W.;Doherty, R. M.; (57) Abraham M.H.; Whitiag, G. S. J. Utromarogr. 1992,594.229-241. Kamlet, M.J. Chromatographla 1988, 25, 373-381. (58) Abraham, M.H. J. Chromarogr. 1993,644,95-139. (47) Hu,2.D.; Hao, X. K. Chromatographla 1993.35, 111-1 13. (59) Abraham, M. H.; Andonian-Haftvan, J.; Hamerton, I.; Poole, C. F.; Kollie, (48) Roses. M.; Bosch, E. Anal. Chim. Acta 1993, 274, 147-162. T. 0.J . Chromarogr. 1993,646, 351-360.
142 Anelyticel chemlsby, Vol. 66, No. 1, &nuary 1. 1994
.
solute
Vlll00
naphthalene iodobenzene chlorobenzene 1,2-dichlorobenzene 1,4-dichlorobenzene bromobenzene 1,1,2,2-tetrachloroethane 1,1,2-trichloroethylene NJV-dimethylaniie benzaldehyde benaonitrile anieole acetophenone phenol nitrobenzene allylbenzene benzyl alcohol, cyclohexanone heptanal 1-phenylethanol o-chlorophenol hexanol p-cresol m-cresol o-dibromobenzene p-chloroacetophenone
0.753 0.671 0.581 0.671 0.671 0.624 0.671 0.492 0.752 0.606 0.590 0.630 0.690 0.536 0.631 0.751 0.634 0.619 0.771 0.732 0.626 0.690 0.634 0.634 0.758 0.780
Kamlet-Taft &meters **2
0.70 0.81 0.71 0.80 0.70 0.79 0.95 0.53 0.75 0.92 0.90 0.73 0.90 0.72 1.01 0.55 0.99 0.76 0.63 0.97 0.74 0.40 0.68 0.68 0.89 0.90
Abraham’s solvation parameters
82
am
Bm
1.0 1.0 1.0 1.0 1.0 1.0 0.5 0.6 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0 0.0 1.0 1.0 0.0 1.0 1.0 1.0 1.0
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06 0.61 0.00 0.00 0.35 0.00 0.00 0.33 0.69 0.45 0.58 0.58 0.00 0.06
0.15 0.05
volume in solid-phase extraction, only the retention properties of the system will be important under reasonable and controlled sampling conditions. The capacity of a solid-phase extraction device only comes into play at high sample concentrations of analyte and/or matrix, and provided that the sample application flow rate is set at a reasonable value and maintained approximately constant during sample processing, the diffusion-related mass-transfer processes only weakly affect the breakthrough volume, at least as far as particle-loaded membranes are con~erned.2~ This means that we need only characterize the retention properties of the sampling system to provide a reasonable estimate of the breakthrough volume. An approach to characterizing the breakthrough volume in terms of easily accessible molecular properties on the one hand and a complementary set of system (fixed) parameters on the other is very attractive because of its predictive capabilities. The breakthrough volumes for additional compounds can then be calculated simply from their characteristic solute properties. A model which enables this to be achieved within the framework of intermolecular forces is doubly valuable because of the insight it provides into the optimization of sorbent properties for different sampling problems. The retention properties of a sampling system under defined operating conditions are amenable to description by a linear model combining the individual intermolecular contributions to the retention process. The simplest models for such a process are the solvatochromic and solvation parameter models based on eqs 4 and 5. The complementary parameters which characterize the properties of the system can be derived from the variation in an observed property (in this case the breakthrough volume) for a series of compounds of known solvation characteristics (explanatory variables) using the mathematical technique of multiple linear regression analysis. The accuracy of the model can be tested statistically. In establishing the model coefficients, it is necessary that the
1% VB 3.230 2.875 2.279 2.929 2.903 2.439 2.097 1.978 2.439 1.477 1.544 2.079 2.000 0.544 1.699 3.279 1.00 1.477 3.000 1.544 1.477 2.278 1.352 1.352 3.279 2.602
0.07
0.03 0.03 0.06 0.10 0.05 0.43 0.44 0.37 0.33 0.49 0.33 0.30 0.20 0.52 0.53 0.41 0.55 0.23 0.33 0.34 0.34 0.02 0.45
vx/100
R2
4
1.085 0.975 0.839 0.961 0.961 0.891
1.340 1.188 0.718 0.872 0.825 0.882 0.596 0.524 0.957 0.820 0.742 0.708 0.818 0.805 0.871 0.717 0.803 0.403 0.140 0.784 0.853 0.210 0.820 0.820 1.190 0.955
0.92 0.82 0.65 0.78 0.75 0.73 0.76 0.37 0.84 1.00 1.11 0.75 1.01 0.89 1.11 0.60 0.87 0.86 0.65 0.83 0.88 0.42 0.87 0.88 0.96 1.09
0.880
0.715 1.098 0.873 0.871 0.916 1.014 0.775 0.891 1.096 0.916 0.861 1.111 1.057 0.897 1.013 0.916 0.916 1.066 1.136
a;
g’H
0.00 0.00 0.00 0.00 0.00 0.00 0.16
0.20 0.12 0.07 0.04 0.02 0.09 0.12 0.03 0.41 0.39 0.33 0.29 0.48 0.30 0.28 0.22
0.08
0.00 0.00 0.00 0.00 0.00 0.60 0.00 0.00 0.33 0.00 0.00 0.30 0.32 0.37 0.57 0.67 0.00 0.00
0.56 0.56
0.45 0.66 0.31 0.48 0.31 0.34 0.04 0.44
Tabk 5. Modal C o d f k h b and Statkticrfw the FH of the MLRA MOW#Used To Chrract.rlre the Rterkthrwgh V o k n m
model Coeff m 5
a
b C
solvation parameter model (Abraham)
solvatochromic model (Kamlet-Taft)
All Solutes in Table I1 4.88 (10.24) -0.91 (10.13) -1.15 (10.13) -2.13 (10.15) -1.01 (h0.25)
6.49 (10.23) -1.16 (10.12) -1.21 (10.08) -2.01 (10.10) -0.54 (10.18)
statistics r 0.989 0.996 atd error 0.117 0.081 F 243 513 After Removing Solutes Showing Poor Agreement in Abraham’s Model m 5.14 (10.17) 6.55 (10.22) 8 -0.92 (10.08) -1.22 (10.11) a -1.05 (10.08) -1.27 (10.07) b -2.24 (10.10) -1.90 (10.10) C -1.23 (10.17) -0.53 (10.17) statistics r 0.996 0.996 std error 0.070 0.070 F 594 587
test solutes are sufficient in number and varied in character to adequately define all specific interactions represented in the model. The accuracy with which the model coefficients can be defined, of course, ultimately depends on the accuracy with which theexplanatory variables are known. In this paper, we have chosen two sets of established explanatory variables and used them to calculate the model coefficients for the range of solutes indicated in Table 2 with the breakthrough volume as the dependent variable. The model coefficients and statistics for the fit achieved with both models are summarized in Table 3. The term containing 62 in the Kamlet-Taft solvatochromic model and the term containing R2 in Abraham’s solvation parameter
/
4~
2 1
3.
/
1'1 / o0w
1 2 3 CALCULATED VALUES
0.8 1
4
Flguro 1. Experimental breakthrough volume vs calculated breakthrough volume using the soivatlon parameter model. The analytes identlRedasshowingpooragreementwlththemodelarecyckhexenone (l), N,Ndlmethylanlllne (2), naphthalene (3), and hexanol (4).
model were found to be statistically insignificant and were removed from the models. In both cases, the truncated models show a good fit to the experimental data with the solvatochromic model giving statistically the better fit of the two models when all the data are considered. A plot of the experimental breakthrough values against the calculated breakthrough values for Abraham's solvation parameter model (Figure 1) indicates that cyclohexanone ( 0.22 log unit), naphthalene (0.21 log unit), N,N-dimethylamine ( 0.14 log unit), and hexanol (0.18 log unit) show a greater deviation between the experimental and the predicted results than is typical for the data set as a whole. N,N-Dimethylaniline is also discordant with the data for the solvatochromic model; the other three compounds show acceptable agreement. For both models, the predicted breakthrough volume for N,Ndimethylamine is greater than the experimental result. This cannot be explained, therefore, by invoking additional retention of the solute through ion-exchange interactions with ionized silanol groups that are not represented in the model, nor can the results simply be dismissed as an experimental error since the experimental results are repeatable. However, in terms of fitting the experimental data to both models, the removal of N,N-dimethylaniline can be justified to improve the basis of the fit with the caveat that in applying the model to compounds similar in type to N,N-dimethylaniline the predictions obtained will not be as reliable as for other compounds. Since cyclohexanone, naphthalene, and hexanol show acceptable agreement in the solvatochromic model, then the deviations observed in the solvation parameter model must be related to the accuracy with which the explanatory variables for these compounds are fixed at the present time. Removal of these compounds one at a time along with N,N-dimethylaniline reveals that the two models show virtually identical predictive properties if the data for N,N-dimethylaniline, cyclohexanone, and naphthalene are removed (Table 3). (Removing or retaining hexanol has no significant influence on the fit to the proposed models.) In deciding which of the two models to use, other considerations are worthy of mention. The molecular volume term in the Kamlet-Taft model is computer generated using programs that may not be readily accessible to everyone.60 144 Analytcal Chemistfy, Vol. 66, No. 1, Jenuary 1, 1994
0.4 0.7
0.8
0.9
1 .o
1.1
1.2
CHARACTERISTIC VOLUME
Flguro 2. Computergenerated Intrinsic molecular volume vs characteristic volume calculated accordlng to McGowan, both divided by 100.
The characteristic volume used by Abraham is calculated by a trivial algebraic expression and is thus accessible to all. At least for simple molecules the two molecular volume terms are well correlated, as indicated by Figure 2 and eq 6, and the
VI= 1.2 + O.SSlV,
r2 = 0.985
n = 25
(6)
characteristic volume could be used to give a first round estimate the intrinsic molecular volume in the absence of the required s o f t ~ a r e . ~ ~(Elimination Jj~ of cyclohexanone and o-dibromobenzene from the correlation considerably improves theagreement betweeen the twodata sets: intercept 1.1; slope 0.680; r2 = 0.992.) Both estimates of the molecular volume are theoretically and technically superior to the molar volume used in earlier work employing the solvatochromic model. The ?r* parameter in the solvatochromic model is obtained from spectroscopic measurements of the absorption bands of selected indicator compounds and is not clearly free energy related. The solvation parameters proposed by Abraham are based on equilibrium measurements and consequently are unambiguously defined as free energy parameters. Also, since the solvation parameters can be calculated from gas and liquid chromatographic experiments, a large number of values for varied compounds are already available (in excess of 1000)38~55-59 and others can be easily estimated from simple combining rules. For compounds not tested by Kamlet and Taft, there is no established protocol to obtain ?r*, am and &. They cannot be obtained from solvatochromic measurements if the compound is a solid, as are many aromatic compounds, and am and pm in any case refer to monomeric compounds (hence the subscript). These factors make the solvation parameter approach of Abraham more amenable to general use in our opinion, although at the present time some revision of certain values for the solvation parameters of some compounds may be required. From an interpretive point of view, both models provide an equivalent picture of the factors influencing the breakthrough volumes on particle-loaded membranes, and therefore, it is unnecessary to describe the results from both models independently. The process characterized by the solvation parameter model is the transfer of the solute between two phases represented (60) Leahy, D. E.J. Pharm. Sci. 1986, 75, 629-636. (61) Kollie. T. 0.; Poole, C. F.J. Chromatop. 1991, 556, 457-484.
TI#. 4. ConWbutlon ot tho DHfoml I n l w " Inlwrctlolllto B"ghVoknndSomeRlp"lrtlv.Canpouwlr compound m(VI/100) m* aam b&
naphthalene nitrobenzene
1-phenylethanol
hexanol p-cresol
anisole acetophenone
4.93 4.13 4.79 4.52 4.15 4.13 4.52
-0.85 -1.23 -1.18 -0.49 -0.83 -0.89 -1.10
-0.42 -0.57 -0.74 -0.08
7
-0.29 -0.57 -1.05 -0.63 -0.65 -0.63 -0.93
by the sample solvent (mobile phase) and the solvated sorbent (stationary phase). The composition of the stationary phase is only poorly defined and cannot be adequately described by the nature of the ligands bonded to the surface alone. Its composition is governed by the surface propertiesof the sorbent, which in turn depends on the concentration of bonded-phase ligands and their structure, concentration of accessible silanol groups, and selective solvation of the surface by solvent molecules, creating a layer of solvent of composition that is likely enriched in organic solvent compared to the bulk sample solvent, and of a thickness that depends on the extent to which the properties of the surface are able to influence the interactions and organization of the solvent molecules in their immediate vicinity. It is reasonable to assume that the properties of the stationary phase remain reasonably constant at low analyte and matrix concentration (at least within the regime that breakthrough does not occur due to exceeding the capacity of the sorbent). Of all the model coefficientsin Table 3, the m coefficient is the only one with a positive sign. This indicates that the most favorable molecular property for increasing the breakthrough volume is to increase the molecular size, or in other words, breakthrough volumes can be expected to increase with increasing molecular volume for molecules of similar polarity. For an individual analyte, the optimum system for isolation will be the one with the largest value for the m coefficient. The above observations can be interpreted in terms of a cavity model. Retention will occur if the free energy difference between opening a hole in the stationary phase of a suitable size to accommodate the analyte and collapsing a hole of the same size in the sample solvent is favorable. When the sample solvent is water, this will generally be the case. From the perspective of sorbent selection, any feature of the sorbent which contributes to reducing the energy required to create a cavity in the stationary phase will contribute favorably to increasing the breakthrough volume. The solvation and solvatochromic parameter models then provide a quantitative approach that can be used to optimize sorbent characteristics for solid-phase extraction. The model coefficients describing the contribution of dipole/polarizability interactions and hydrogen-bond acid/ base interactions to the breakthrough volume are all negative, indicating that these interactions favor solvationin the sample solvent and reduce the breakthrough volumes for polar compounds in opposition to the influence of their size. For perspective the contribution of the different intermolecular interactions to the breakthrough volume for a few representative compounds is summarized in Table 4. Given that the solutesolvation parameters are scaled to cover a roughly similar range of values, then the primary interaction which reduces
"1 404 0
\A '
'
100
200
300
400
500
SAMPLB VOLUME Flgwo 5. Some representativeplots of the experimentalbreakthrough volume curves for benzaldehyde (A), acetophenone (B), and N,K dimethylaniline (C).
retention is the solute's hydrogen-bond basicity, which is more important than its acidity, and the solute's capacity for dipole/ polarizability interactions, which is much more important for aromatic compounds than for nonaromaticcompounds. These characteristics are directly attributable to the properties of water, which is such a strong hydrogen-bond acid that few species can effectively compete with it. This is why the contribution from the strong hydrogen-bond acids, p-cresol and the alcohols in Table 4, make only a small contribution to the magnitude of the breakthrough volume. These compounds are amphoteric and their hydrogen-bond basicity is just as or more important than their hydrogen-bond acidity in determining the breakthrough volumes. The aromatic compounds have larger ?r* and Om values than their alkane counterparts and for this reason have smaller breakthrough volumes. A sorbent would have to have significantpolarity to compete with water in order to reduce the magnitude of the model coefficients describing the contribution of polar interactions to the breakthrough volume. It is unlikely that for chemically bonded sorbents such an approach would result in large changes in the breakthrough volume. Also, such changes would have to be achieved without increasing the cohesive energy of the stationary phase, which would diminish the value for the m coefficient by increasing the free energy required for cavity formation. Since the m coefficient is the dominant term in the solvation model for controlling the breakthrough volume, any process which reduces its contribution to the breakthrough volume is undesirable. This would tend to suggest that polar bonded-phase sorbents might be less useful for isolating analytes from water than from a totally nonselective phase. The solvation models proposed here provide a direct approach to answering this question in an unambiguous manner after generating the necessary experimental data. Given the difficulty in obtaining breakthrough volumes with the kind of accuracy that can be achieved by determining retention in column liquid chromatography, the agreement observed for the experimental results and the solvationmodels is very good and certainly adequate for predictive purposes. Some typical experimental breakthrough curves are shown in Figure 3. There is obviously a certain degree of arbitrariness in the detection of the breakthrough point, which initially does not represent a large change in the amount of analyte Analytfcai ChemMy, Voi. 66, No. 1, January 1, 1994
145
recovered. For each experiment, several new disks are used so superimposed on the results is a contribution from the variability between individual disks. Within the experimental design, sample volumes were chosen in increments of 2.5 mL for breakthrough volumes in the range 0-50 mL, 5 mL for 50-100mL, 10mLfor 100-1000mL,and lOOmLfor>lOOO mL once a rough estimate of the breakthrough volume had been established. Since it is impossible to interpolate between experimental points to find the breakthrough volume, the difference between the amount of analyte recovered between two points and the general trend in the experimental breakthrough curves was used to establish the breakthrough volume. Consequently, the estimate of the breakthrough volume contains a variable error on a percentage basis equivalent to some fraction of the volume measurement increment for the experiment and the absolutevalue of the breakthrough volume.
146
Anelytical Chemkby, Vd. 66,No. 1, January 1, 1994
Within these constraints, the agreement represented by the fit of the model equations in Table 3 is very good and certainly adequate for the assessment of a safe sampling volume for a target analyte. Finally, the availability of a reliable method for the prediction of breakthrough volumes that can be derived from molecular parameters provides insight into the retention process that underlies the sampling capacity of a solid-phase extraction device and obviates the need for the slow and tedious experimental measurement of breakthrough volumes for each new analyte encountered. It also offersa quantitative approach to characterizing and optimizing the retention properties of sorbents used in solid-phase extraction. Received for review M a y 25, 1993. Accepted October 1, 1993.. Abstract published in Advance ACS Absrracrs, November 1, 1993.
