High-Performance Capillary Gel Electrochromatography with

Anal. Chem. 1998, 70, 4985-4995

High-Performance Capillary Gel Electrochromatography with Replaceable Media Mark R. Schure,*,† Robert E. Murphy,‡,§ Wendy L. Klotz,‡ and Willie Lau|

Rohm and Haas Company, 727 Norristown Road, Spring House, Pennsylvania, 19477

Capillary gel electrochromatography is evaluated with an entangled polymer solution which is pumped into the capillary and run under fritless conditions. The polymer used has an acid backbone with grafted hydrophobic segments, the polyacid giving the electroosmotic flow and the hydrophobe segments providing the retentive component. Experimental evaluation of this type of system reveals performance similar to capillary electrophoresis and other forms of electrochromatography. The analysis of plate height data demonstrates that zone broadening is primarily due to diffusion with little contribution from nonequilibrium zone broadening. Hence, operation at high velocities (high voltages) is most desirable as opposed to most chromatographic methods. Some of the advantages of this type of experiment include being able to replace the retentive media in a few minutes, fast and reproducible high-performance separation, and having a retention mechanism similar to reversed-phase liquid chromatography. Disadvantages include a low retentive phase concentration and hence low sample loadability and limited solvent compatibility of the polymer. A number of different separations are demonstrated including separation of alkyl benzoates, alkylphenones, alkylbenzenes, oxidation inhibitors, and PAHs. A number of techniques now exist that are variations of the capillary electrophoresis (CE) experiment, and these are rapidly becoming well established additions to the basic CE methodology. These include micellar electrokinetic chromatography (MEKC) and capillary gel electrophoresis (CGE). These variations differ in the mechanism of separation and the chemical nature of material inside the capillary. For example, in MEKC, the mechanism is that of retention of solute inside a micelle, resembling the two-phase interactions commonly found in chromatography. The mass transport of solute in the retentive phase is due to electrophoretic movement of the micelle. In CGE, the solute selectivity is achieved through differences in the molecular size, somewhat resembling that found in size exclusion chromatography. Zone movement, however, is due to electrophoresis through the gel pores. †

Theoretical Separation Science Laboratory. Analytical Research. § Present address: Isis Pharmaceuticals, Inc., Carlsbad Research Center, 2292 Faraday Ave., Carlsbad, CA 92008. | Exploratory Polymer Research. ‡

10.1021/ac980719d CCC: $15.00 Published on Web 11/04/1998

© 1998 American Chemical Society

Another variation on the basic capillary format of CE is the electrochromatography (EC) technique. In EC, retention of solute in some form of stationary retentive phase provides the selectivity for separation as is the case for a normal chromatographic separation. However, in EC, the fluid-mediated transport of solute is through electroosmotic flow, which is provided by the support material that holds the retentive phase. The interest in EC stems from the belief that zone broadening is generally smaller because the flow profile is uniform and that flow can be achieved with smaller particles. Uniform flow profiles and smaller particles lead to higher resolution, which is very desirable in complex analysis or in situations where the zone width can be compromised to run at faster analysis time. This is in contrast to the parabolic flow profile found in pressure-driven flow from a pump-driven packed bed chromatographic experiment. In this case, small particles can cause huge pressure drops in the packed bed, which leads to pump fatigue and shorter column lifetime. The EC technique has been implemented in a number of ways in the past. These implementations include capillaries packed with small particles1-4 and capillaries used in the open-tube configuration5-7 although other methods such as thin-layer chromatographic plates operated under electrochromatographic conditions have also been reported.1 It is very desirable to run the EC technique with very small particle diameter so that zone broadening is minimized. In normal packed bed chromatography, pressure-driven flow yields large pressure drops when small particles are used. This is not an issue in EC, because electroosmotic flow can easily be established in porous media with very small pore size and with no deleterious heating or pressure effects. However, when very small particles are used in packed bed EC, sample preparation must be extremely rigorous to prevent impurities from clogging particle interstitial regions. Other problems exist for EC in the open-tube configuration5-7 which include the lack of abundant retentive phase per column length and small performance increase as compared with pressure-driven flow using a micro-LC column. (1) Pretorius, V.; Hopkins, B. J.; Schieke, J. D. J. Chromatogr. 1974, 99, 2330. (2) Jorgenson, J. W.; Lukacs, K. D. J. Chromatogr. 1981, 218, 209-216. (3) Knox, J. H.; Grant, I. H. Chromatographia 1991, 32, 317-328. (4) Yan, C.; Dadoo, R.; Zhao, H.; Zare, R. N.; Rakestraw, D. J. Anal. Chem. 1995, 67, 2026-2029. (5) Tsuda, T.; Nomura, K.; Nakagawa, G. J. Chromatogr. 1982, 248, 241-247. (6) Bruin, G. J. M.; Tock, P. P. H.; Kraak, J. C.; Poppe, H. J. Chromatogr. 1990, 517, 557-572. (7) Tan, Z. J.; Remcho, V. Anal. Chem. 1997, 69, 581-586.

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The packed capillary configuration has recently been augmented by new retentive phases. These include capillaries packed with in situ polymerized sol-gel media,8,9 in situ polymerized polyacrylamide gel material,10-12 and in situ polymerized stearyl or butyl methacrylate gel.13 The term “monolithic columns”14,15 has been used to describe materials that are polymerized inside the capillary and form one continuous porous material throughout the capillary length. This type of media has various levels of chromatographic performance and requires different levels of expertise for preparation. In addition, because these systems are prepared in situ, their use depends on the ease of cleaning the freshly prepared capillary prior to stable analytical utilization. Because the pore space is small in these systems, they appear to be very susceptible to clogging. Once clogged, the lifetime of the capillary is reached and a new capillary must be used. Irreversible adsorption will reduce the electroosmotic velocity for this and other types of EC. This is contrasted to normal pressure-driven flow LC where the driving velocity is not affected by irreversible adsorption. The configurations mentioned above utilize very small interstitial lengths; this facilitates the reduction or elimination of all of the chromatographic mass transport terms from the plate height equation. Hence, these monolithic systems strive for a strictly diffusion limited plate height, much like the case in open-tube capillary electrophoresis, only with a chromatographic separation mechanism (for example, partitioning and/or adsorption) for enacting the separation. This point has been made previously in theoretical papers.16,17 Although CGE was originally conducted with cross-linked media (usually polyacrylamide), much more versatility and ease of use was found by employing entangled polymer solutions18 which utilized hydroxyethyl cellulose (HEC), linear polyacrylamide, or poly(ethylene oxide) (PEO). In an analogous fashion, it is very desirable to form a gel material that is not cross-linked and perform a capillary electrochromatography experiment with an entangled polymer solution. We shall show this type of experiment in this paper. There is a type of polymer that may be ideally suited for implementation of this form of electrochromatography: polyelectrolytes with grafted hydrophobic ligands. More specifically, there are examples in the literature of polyelectrolytes with acrylic,19 sulfonic,20 and other acid backbones grafted with hydrophobic segments that contain alkyl groups of 12 carbons and longer. These polymers are employed in a number of applications, such (8) Guo, Y.; Colo´n, L. A. Anal. Chem. 1995, 67, 2511-2516. (9) Guo, Y.; Colo´n, L. A. J. Microcolumn Sep. 1995, 7, 485-491. (10) Fujimoto, C.; Kino, J.; Sawada, H. J. Chromatogr., A 1995, 716, 107-113. (11) Fujimoto, C. Anal. Chem. 1995, 67, 2050-2053. (12) Fujimoto, C.; Fujise, Y.; Matsuzawa, E. Anal. Chem. 1996, 68, 2753-2757. (13) Liao, J.-L.; Chen, N.; Ericson, C.; Hjerte´n, S. Anal. Chem. 1996, 68, 27532757. (14) Peters, E. C.; Petro, M.; Svec, F.; Fre´chet, J. M. J. Anal. Chem. 1998, 70, 2288-2295. (15) Peters, E. C.; Petro, M.; Svec, F.; Fre´chet, J. M. J. Anal. Chem. 1998, 70, 2296-2302. (16) Knox, J. H.; Grant, I. H. Chromatographia 1987, 24, 135-143. (17) Schure, M. R.; Lenhoff, A. M. Anal. Chem. 1993, 65, 3024-3037. (18) Grossman, P. D. In Capillary Electrophoresis, Theory and Practice; Grossman, P. D., Colburn, J. C., Eds.; Academic Press: San Diego, CA, 1992; Chapter 8. (19) Lockhead, R. Y. In Polymers as Rheology Modifiers; Schulz, D. N., Glass, J. E., Eds.; ACS Symposium Series 462; American Chemical Society: Washington, DC, 1991; pp 101-120.

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as rheology modifiers.19 In this application they are generally referred to as associative thickeners. The rheological application mechanism is established by allowing the acid backbone to impart water solubility and the grafted hydrophobe to establish a sticky contact point so that intermolecular interactions drive an increase in solution viscosity through the formation of a transient polymer network. For the case of electrochromatography, the acid backbone is used as a charge center for associated cations so that an electroosmotic flow can be established when an electric field is applied. The grafted hydrophobes can act as the retentive center. Since the length and molecular weight of these hydrophobically modified polyelectrolytes are large, the polymer can be pumped into the capillary as an entangled gel. Due to entanglement and possibly some hydrogen bonding with the silica capillary wall, no frit system is utilized for this form of capillary gel electrochromatography(CGEC). The synthesis of these polymers is external to the capillary, promoting a minimum of capillary conditioning. This has a distinct advantage in both time and convenience. In this paper, we describe experiments utilizing this type of polymer for CGEC. In this way, transport and selective retention occur on length scales on the order of tens of angstroms. We discuss the practical advantages and disadvantages of this approach and demonstrate a number of applications which illustrate the speed and resolution that is possible with this technique. THEORY Phase Density. In conventional HPLC packed columns, the concentration of bonded phase can be expressed as Cv ) AmFsFb, where Cv is the concentration of bonded phase with units of micromoles per milliliter of column. Additionally, Am is the mass specific surface area of the packing with units of square meters per gram, and Fb is the bonded phase density with units of micromoles per square meter. The superficial density of the packing, Fs, is the reciprocal of the observed volume of particles per unit mass; Fs has units of grams per milliliter. The superficial density can be expressed in terms of the bulk material density, F, via Fs ) F(1 - ),where  is the fraction of total column volume contained external to the surface of the particle. Note that  ) b + (1 - b)p, where b is the fraction of column volume contained in the interstitial region and p is the fraction of particle volume contained in the particle pore. Typical values of b are 0.4 21 and typical values of p range between 0.3 and 0.7.21 Hence, for parameters typical of a silica packing material Am ) 200 m2 g-1, F ) 2.2 g mL-1, Fb ) 4 µM m-2, and  ) 0.8, so that Cv ) 352 µM bonded phase per milliliter of column. This result is compared first with a wall-coated capillary column where the retentive phase is bonded to the capillary surface and then to the case of a polymer with grafted hydrophobe in solution, as is the case studied in this paper. For the wall-coated capillary, Cv ) 4Fb/d, where d is the capillary diameter in micrometers, and the other quantities have their previous meanings and units. For a 50-µm-diameter capillary and Fb ) 4 µM m-2, Cv ) 0.32 µM (20) Morishima, Y. In Multidimensional Spectroscopy of Polymers, Vibrational, NMR, and Fluorescence Techniques; Urban, M. W., Provder T., Eds.; ACS Symposium Series 598; American Chemical Society: Washington, DC, 1995; pp 490-516. (21) Guiochon, G.; Golshan-Shirazi, S.; Katti, A. M. Fundamentals of Preparative and Nonlinear Chromatography; Academic Press: New York, 1994.

bonded phase per milliliter of column, showing a greatly reduced capacity for solute as compared with the packed column. This result is qualitatively well understood for the wall-coated capillary chromatography experiment where overloading effects are known and are reflected in a factor of ≈1000 reduction in volumetric phase capacity from that of a packed bed column. We now examine the situation for CGEC and specifically for a polymer with grafted hydrophobe, as used in this paper. We will assume here that the polymer is in the spherical random coil state22,23 with concentration at the entanglement threshold where random coil segments begin to overlap. The volume encompassed by a polymeric spherical segment is Vp ) 4/3πRg3, where Rg is the radius of gyration.22,23 Due to packing constraints, and assuming that these spherical segments do not overlap or deform, the total volume taken up by an array of these spherical segments will be greater than Vp by a factor 1/f, where f g 0.6. The value f ) 0.6 corresponds to the random loose packing limit,24 f ) 0.74 is for face-centered cubic crystal packing, and f ) 1 corresponds to the case where deformation occurs so that a continuous polymer gel is formed but there is no physical entanglement. The effective occupational volume of polymeric material, Vo, is therefore equal to Vp/f. Given a polymer chain of Nt monomer units, where the average number of monomer units between hydrophobe grafting centers is designated as N h bh, there will be N h gh ) Nt/N h bh grafted hydrophobe segments per polymer chain. Hence, the number concentration of hydrophobe chains per unit volume is given approximately as N h gh/Vo. Converting this to units of micromoles per milliliter of column yields

Cv )

Nt f N h bhR3g

× 3.96 × 10-7

(1)

where Rg has units of micrometers, and again Cv has units of micromoles per milliliter. For many of the polymer systems we have examined Nt ) 5000, N h bh ) 50, f ) 0.60, and Rg ) 0.1 µm. Using these numbers, eq 1 gives Cv ) 2.4 × 10-2 µmol/mL. This suggests that the solute capacity of capillary gel electrochromatography is less than wallcoated capillary chromatography by a factor of ≈13 and less than a packed column by a factor of ≈15 000. These comparisons have been made on a moles of retentive phase per volume of column basis. The comparison can also be made on a moles of retentive phase per unit column length basis, Cl, by multiplying Cv by the column volume per unit length. This comparison is perhaps more relevant for technique comparison. A conventional HPLC column discussed above with 4.6-mm inner diameter will have Cl ) 59 µM bonded phase per centimeter of column length. A packed electrochromatography column with a 50-µm inner diameter will have Cl ≈ 7000 pmol of bonded phase per centimeter of column length. For the wall-coated capillary with a 50-µm inner diameter, Cl ≈ 6 pmol of bonded phase per (22) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Oxford University Press: New York, 1989. (23) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1988. (24) German, R. M. Particle Packing Characteristics; Metal Powder Industries Federation: Princeton, NJ, 1989.

Table 1. Summary of Phase Density Calculations retentive-phase concn column type

per volume (µM mL-1)

per length

packed conventional borea packed microboreb wall-coated open-tube capillaryb capillary gel electrochromatographyb

352 352 0.32 0.024

59 µM cm-1 7000 pM cm-1 6 pM cm-1 0.5 pM cm-1

a Column internal diameter, 4.6 mm. b Capillary internal diameter, 50 µm.

centimeter of column length. For capillary gel electrochromatography in a 50-µm-inner diameter capillary, Cl ≈ 0.5 pmol of retentive phase per centimeter of column length. These calculations are summarized in Table 1. These calculations are approximate because the polymer segments may be quite entangled as discussed in the rheological experiments described below. However, these calculations suggest that there is significantly less phase present in this form of electrochromatography as compared to a packed column experiment. Because of the proportionally lower sample capacity, detection may be more difficult. This concern has, however, been addressed by both the CE and microcolumn LC communities previously. EXPERIMENTAL SECTION Synthesis. The polymer was composed of 40% ethyl acrylate, 50% methacrylic acid, and 10% lauryl methacrylate. It was synthesized by emulsion polymerization25 using methyl β-cyclodextrin as a phase transport catalyst.26 The polymerization was carried out in a reaction flask equipped with a mechanical stirrer, temperature control device, condenser, monomer and initiator feed lines, and a nitrogen inlet. Deionized water (570 g), sodium lauryl sulfate (5.4 g), and methyl β-cyclodextrin (3.1 g) were introduced into the reaction flask at room temperature. The contents of this flask was heated to 83 °C while stirring under a nitrogen purge. The monomer emulsion was prepared by the homogenization of deionized water (405 g), sodium lauryl sulfate (5.4 g), and a monomer mixture at room temperature. The monomer mixture contained ethyl acrylate (268 g), lauryl methacrylate (67 g), and methacrylic acid (335 g). At 83 °C, ammonium persulfate (0.7 g) dissolved in water (6 g) was introduced into the reaction flask. The monomer emulsion was co-fed into the reaction flask over 100 min together with an initiator solution consisting of ammonium persulfate (0.3 g) in water (100 g). At the end of the feed, the reaction mixture was held at 83 °C for 15 min followed by cooling under ambient conditions. Upon cooling to room temperature, the polymer was filtered through a 100-mesh screen. The total solids content of the polymer dispersion was measured at 36.1%, and the conversion was essentially quantitative. Chemicals and Postsynthesis Procedure. An ultrafiltration device from Amicon (Beverly, MA) equipped with a 10 000-Da cutoff filter was used to remove any low-molecular-weight additives and impurities that were present. The polymeric material was (25) Emulsion Polymerization and Emulsion Polymers; Lovell, P. A., El-Aasser, M. S., Eds.; John Wiley and Sons: New York, 1997. (26) Lau, W. U.S. Patent 5,521,266, 1996.

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Figure 1. Chemical structures of the solute molecules used in this study.

rinsed and filtered three times to reduce these impurities ≈1000fold. The resulting purified polymer solution was freeze-dried with a Labconco (Kansas City, MO) freeze-dryer to give a solid, which was stored until needed. The water used for these processes and the electrochromatography buffers was obtained from a Milli-Q water system (Millipore Corp., Milford, MA). Experiments were conducted at pH 9.1 and pH 11.3. The pH 9.1 buffer was composed of 10 mM sodium tetraborate decahydrate in the acetonitrile/water mixture. The pH 11.3 buffer was made with sodium phosphate dibasic and sodium phosphate tribasic and then diluted to the final organic concentration with HPLC-grade acetonitrile from J. T. Baker (Phillipsburg, NJ). The polymer was prepared for electrochromatography by adding it in the solid form directly to these buffers at the various reported concentrations. All of the analytes were purchased from Aldrich Chemical Co. (Milwaukee, WI) and used without further purification. The molecular structures of solutes used in this study are shown in Figure 1. The sources of the chemicals used in the synthesis procedure were as follows. Ethyl acrylate, lauryl methacrylate, and methacrylic acid were obtained from the Rohm and Haas Co. (Philadelphia, PA). Ammonium persulfate was from Aldrich, methyl β-cyclodextrin was from Wacker-Chemie (Munich, GmbH), and sodium lauryl sulfate was from the Stepan Co. (Northfield, IL). Polymer Characterization. Characterization of the polymer following synthesis was accomplished primarily by size exclusion chromatography (SEC) with standards of similar composition and by light scattering using a BI-90 instrument (Brookhaven Instruments Corp., Holtsville, NY). The molecular weight of the 4988 Analytical Chemistry, Vol. 70, No. 23, December 1, 1998

polymer was found to be ≈1 million. Liquid chromatography and electrical field-flow fractionation have also been used to characterize the polymer.27 CE Instrumentation. A Hewlett-Packard (Wilmington, DE) 3D capillary electrophoresis system was used for all experiments. Fused silica capillary tubing (50-µm i.d.) was obtained from J&W Scientific (Folsom, CA). Unless otherwise specified, all capillary lengths were 50 cm, resulting in a distance of 42 cm between injector and detector. All experiments were conducted with the temperature set to 25 °C. The injection end of the capillary was electrically positive with respect to the polarity at the detection end. Hence, the analytes were convectively driven toward the detector by electroosmosis of the positively charged acid protons. The instrument was operated in the constant-voltage mode with typically 30 kV applied across the capillary, resulting in a typical field strength of 600 V cm-1 unless otherwise specified. The detector was set at 200 nm with a reference wavelength of 225 nm and a response time of 0.1 s. Electrokinetic injection of the sample was at 1 kV for 30 s unless otherwise specified. Prior to each set of runs (once a day), the capillary was rinsed with buffered polymer solution for 30-60 min. The polymer gel has reduced viscosity (shear thinning) when the pressure is applied during filling of the capillary and the gel flows into the capillary. Thus, the polymer solution may disentangle slightly during capillary filling. After filling, a hold period of 30 min was used for the gel to reestablish entanglement before the analyses are initiated. The migration times and peak width at half-height were determined with the HP ChemStation software using an average of at least three replicate injections. The reproducibility of migration times was typically less than 1% relative standard deviation. Viscosity Measurements. A Rheometrics fluid spectrometer II (Rheometrics, Piscataway, NJ) was used for all viscosity measurements. The testing geometry used was cone and plate (50-mm diameter, 0.02-rad angle cone). Measurements were made at ambient room temperature (23-24 °C). RESULTS AND DISCUSSION Polymer Concentration. Figure 2 shows the electrochromatograms of a methyl, ethyl, propyl, and butyl benzoate mixture at various concentrations of the retentive phase. As can be seen from Figure 2A, no separation is obtained at zero polymer concentration. Also note that the solute elutes at ≈4.35 min with an electroosmotic velocity of 0.161 cm s-1. Little separation is noted to occur in Figure 2B, where the polymer concentration, Cp, is 0.98 wt %. However, it can be seen that now the elution time is shorter due to the presence of enhanced electroosmotic flow. As discussed below in the section on system peaks, if the first negative peak is used as an indication of the fluid velocity, then the electroosmotically driven fluid velocity is now 0.226 cm s-1. This demonstrates that the polymer does cause electroosmotic flow to occur above that exhibited by the capillary wall electroosmosis. (27) Palkar, S. A.; Murphy, R. E.; Schure, M. R. In Particle Size Distribution III: Assessment and Characterization; Provder, T., Ed.; ACS Symposium Series 693; American Chemical Society: Washington, DC, 1998.

Figure 3. Low-shear viscosity as a function of the weight percent of polymer in solution, Cp. Figure 2. Separation of (1) methyl, (2) ethyl, (3) propyl, and (4) butyl benzoate at 0, 0.98, 1.97, 3.11, and 3.72 wt % polymer concentration. The solvent conditions are 40:60 acetonitrile/water at pH 11.3. The run-time voltage is 30 kV with an electokinetic injection of 5 kV for 15 s.

Further resolution is noted to occur when Cp ) 1.97%, as shown in Figure 2C. Also shown in this figure is the reduction in electroosmotic flow velocity (0.209 cm s-1) as compared to that shown in Figure 2B. One explanation for this reduction is that as the gel concentration is increased, the effective pore size between adjacent chain entanglements decreases. This reduction has been expressed for polymers18,23 as ξ ∼ Cpl, where ξ is the pore size, l is the scaling exponent, which has a value of ≈-0.7, and the symbol “∼” is read as “scales as”.23 With decreasing pore size, the counterion double layer from each acid site overlaps to an increasingly greater extent with neighboring double layers. As this overlap increases, the electroosmotic velocity quantitatively decreases.28 The broad peak seen in Figure 2C at 4.7 min may be due to some retained solute component(s); however, the formation of the polymer network at this polymer concentration may not be stable which could cause solute splitting. This point is speculative, and since this concentration region is not useful from an analysis standpoint, we have not studied this effect further. The resolution increases as Cp is increased from 3.11 to 3.72%, as shown in Figure 2D and E. Also note that the electroosmotic flow velocity, as judged by the system peak elution time, decreases further. In the peaks shown in Figure 2E, there is full baseline resolution in less than 5 min. The peak widths are particularly small here; for the separation shown in Figure 2E, the peak width at half-height for butyl benzoate (the most retained peak) is 1.93 s, which is a Gaussian standard deviation of 0.822 s. For a retention time of 4.807 min, the number of theoretical plates is ≈123 000 or ≈293 000 plates/m. Rheology. In an effort to explain some of the results shown in Figure 2, we have examined the viscosity and shear rate dependence on viscosity in the concentration region of polymer used in Figure 2. These results are shown in Figure 3 for the viscosity, η, as a function of mass percent of polymer in solution and in Figure 4 where the viscosity η is plotted as a function of (28) Rice, C. L.; Whitehead, R. J. Phys. Chem. 1965, 69, 4017-4024.

Figure 4. Viscosity as a function of shear rate for various concentrations of polymer solution.

the shear rate used to make the measurements. Note that η0 is the viscosity of the buffer solution which does not contain polymer. The value of η0 is ≈0.01 P, which is within measurement error the same as the viscosity of pure water, which is 0.010 002 P at 20 °C. The viscosity measurements shown in Figure 3 are obtained by utilizing the smallest values of the shear rate data. As can be seen in Figure 4, the shear rate dependence on η is dominant over the whole experimental range. The shear measurements suggest that the data in Figure 3 may be in error because the viscosity measurements are not independent of shear effects even at the lowest shear rates. In addition, the viscosity appears to monotonically decrease as higher shear rates are applied. This behavior, which is known as shear thinning,29 is common for many polymers and polymer solutions29 and suggests that the dynamics of polymer entanglement are slow compared to the rates of shear used in performing these rheological measurements. As shown in Figure 3, η increases monotonically over the range 0 e Cp e 0.75%. A common interpretation of this behavior30 is that interpolymer interactions are minimal here and that additional polymer simply creates additional solution drag, as in the classical viscosity laws for dilute solutions.30 For Cp > 0.75%, the viscosity (29) Macosko, C. W. Rheology Principles, Measurements, and Applications; VCH Publishers: New York, 1994. (30) Barrat, J.-L.; Joanny, J.-F. In Advances in Chemical Physics; Prigogine, I., Rice, S. A., Eds.; John Wiley and Sons: New York, 1996; Vol. XCIV, pp 1-66.

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decreases until Cp ≈ 2.5%, at which point the viscosity starts to increase again. The concentration domain 0.75% e Cp e 2.5% is interpreted as a region where polymer entanglement takes place, and as shown in Figure 2, electroosmotic flow can now proceed in the pore network. Figure 2 shows that separation is just starting to become visible at Cp ) 0.98% and is well established at Cp ) 1.97%. These entanglements are most likely not very strong. However, the decreasing of the viscosity shown in Figure 3 may be due to continuous changes in the polymer conformation, driven by the strong charge repulsion between polymer backbone segments. This repulsion mechanism may minimize interpolymer interaction until physical overlaps become statistically dominant and/or hydrophobe association contributes to the interpolymer association. This reduction in viscosity with increasing polymer concentration has been observed in polyelectrolyte systems previously;30 however, this behavior is not fully understood. At Cp > 3% the viscosity starts to increase and near Cp > 4% the solubility limit of polymer is reached. Although not shown in Figure 3, as the solubility limit concentration is approached, η increases rapidly. We find that the most efficient and desirable separations occur in this region, as seen in Figure 2. The polymer in this concentration region may have an entangled state where hydrophobic association between hydrophobic segments is contributing additionally to the viscosity. Although we show the rheological results of the higher pH experiments, the lower pH experiments using the borate buffer show the same trends as the higher pH results. However, the viscosities are somewhat higher for the lower pH rheology. This may be due to less solubility per polymer at lower pH, more intermolecular and intramolecular hydrogen bonding between undissociated acid groups at lower pH, or both. Plate Heights. Plate heights are obtained by utilizing the CE instrument software calculation of the peak width at half-height. This number is then divided by (8 ln 2)1/2 to get the Gaussian standard deviation, σ. Plate height H is then calculated via H ) Lσ2/tr2, where tr is the time of the peak maximum and L is the capillary length from injector to detector. To calculate H as a function of the average fluid velocity 〈ν〉, the field strength is varied and the measurement of 〈ν〉 is taken from the first system peak. The field strength is varied by using run-time voltages which range from 5 to 30 kV in 5-kV increments. Three variations of the van Deemter equation31-33 are used to fit the plate height data using a combination of nonlinear leastsquares minimization algorithms based on the Nelder-Mead Simplex algorithm34 for initial estimates, followed by the Levenberg-Marquardt algorithm35 for final estimates. The three variations of the van Deemter equation used here are H ) A + B/〈ν〉 + C〈ν〉, H ) A + B/〈ν〉, and H ) B/〈ν〉 + C〈ν〉, where A is the eddy diffusion coefficient, B is the molecular diffusion coefficient, and C is the nonequilibrium coefficient. By using these three different forms, we attempt to minimize the number of (31) van Deemter, J. J.; Zuiderweg, F. J.; Klinkenberg, A. Chem. Eng. Sci. 1956 5, 271-289. (32) Giddings, J. C. Dynamics of Chromatography; Marcel Dekker: New York, 1965. (33) Giddings, J. C. Unified Separation Science; Wiley: New York, 1991. (34) O’Neill, R. In Applied Statistics Algorithms; Griffiths, P., Hill, I. D., Eds.; Ellis Horwood Limited: Chichester, England, 1985; pp 79-87. (35) Bevington, P. R. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill Book Co.: New York, 1969.

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Figure 5. Plate height H as a function of velocity v. Conditions are the same as in Figure 2 except the run time voltages are 5-30 kV at 5-kV increments and the electrokinetic injection is 1 kV for 30 s. The polymer concentration is 3.72%. The triangles, open circles, squares, and solid circles represent the results for methyl, ethyl, propyl, and butyl benzoate, respectively. The equations H ) A + B/〈ν〉 + C〈ν〉, H ) A + B/〈ν〉, and H ) B/〈ν〉 + C〈ν〉 are represented by solid, dashed, and dotted lines, respectively.

parameters and discover which effects may be controlling the zone broadening. The plate height data for methyl, ethyl, propyl, and butyl benzoate are shown in Figure 5 along with the results of curve fitting the three models described above. As can be seen from Figure 5, the data for all four solutes appear to fit the full van Deemter equation (solid line) quite well throughout the velocity range. Clearly, in the velocity region studied here, these curves represent the situation where molecular diffusion is the dominating factor in controlling zone broadening. This is similar to the case in capillary electrophoresis where diffusion is the major source of zone broadening although here the mechanism of separation is based on phase equilibria found in chromatography. From Figure 5, we note that all three models fit the data almost equally well. The best curve fits, however, are with the full model H ) A + B/〈ν〉 + C〈ν〉 (solid line) with an average relative standard deviation (RSD) of ≈ 2%. The model H ) B/〈ν〉 + C〈ν〉 (dotted line) fits somewhat better (RSD ≈ 4%) than the model H ) A + B/〈ν〉 (dashed line) with RSD ≈ 6%. Although the original van Deemter model has been questioned because of the lack of coupling between eddy diffusion and mobile-phase nonequilibrium,32,33 it appears that for these experiments the overall model fits well even without the eddy diffusion term. Hence, this distinction is of little concern here because the diffusive behavior (through B/v) is the dominant term. We do note, however, that inclusion of the nonequilibrium coefficient C in the models does improve the fit slightly and appears to be necessary. The mobile-phase nonequilibrium term in a uniform geometry scales as d2, where d is the column or particle diameter.32,33 As d is reduced to the level found in a random coil polymer, i.e., as d approaches the length scale of pore size ξ, the overall contribution of this term is vastly reduced but does not completely disappear

Figure 6. Change in system peaks with variation in the composition of the injection plug for the benzoate mixture separated in Figure 2.

and may become dominant at extremely high field strengths. Resistance to mass transport in the stationary phase should be nearly zero because of the very close distance between retentive sites and electroosmosis-producing sites. In this regard, the highest field strength used in this study (600 V cm-1) does not produce results that are near the minimum plate height H, as shown in Figure 5. Accepting H ) A + B/〈ν〉 + C〈ν〉 as a realistic description of zone broadening, the minimum in H will be found at 〈ν〉 ) (B/C)1/2. Using the parameter estimates from least-squares analysis, the minimum plate height should be obtained at 〈ν〉 ) 0.358 cm s-1 for the methyl benzoate peaks and 〈ν〉 ) 0.232 cm s-1 for butyl benzoate. Thus, even higher field strengths (and velocities) should be considered for this type of experiment as the results presented here are below the estimated optimum velocity. System Peaks. System peaks are present in the electrochromatograms shown in Figure 2 as the first and second peaks. These peaks have their origins in the displacement of equilibrated solvent on the retentive phase and are affected by the solvent mixture composition and by the strength of the retention of solute peaks.21,36-38 We should be able to use these system peaks to gain more information, such as an accurate measure of 〈ν〉, and information about the chemical equilibria in the electroosmotic flow generation process. By varying the chemical composition of the injected sample, we can see a few interesting effects, as shown in Figure 6. Increased water concentration in the sample injection will increase the concentration of the first system peak and decrease the concentration of the second system peak, relative to the run where the injection concentration is the same as the buffer solution. This suggests that the first system peak is due to water and the reestablishment of local equilibrium involving water. Since water is less retained, we use the first system peak as an indicator of the electroosmotic flow under low retention conditions. Increased acetonitrile concentration in the sample injection will split the second system peak, as shown in Figure 6. However, we note the increase in concentration of the second system peak (36) Levin, S.; Grushka, E. Anal. Chem. 1986, 58, 1602-1607. (37) Levin, S.; Grushka, E. Anal. Chem. 1987, 59, 1157-1164. (38) Golshan-Shirazi, S.; Guiochon, G. Anal. Chem. 1990, 62, 923-932.

Figure 7. Separation of alkylphenones. Peaks: (1) acetophenone, (2) butyrophenone, (3) hexanophenone, and (4) octanophenone. Conditions: 5-kV injection for 15 s, 4.00% polymer retentive phase, run voltage 30 kV, and solvent 40% acetonitrile at pH 9.1. The injection concentration of each compound is 400 ppm.

and the decrease in the “observable” first system peak. This helps in identifying the second system peak as the redistribution of local equilibrium for acetonitrile and may indicate that there is retention of acetonitrile by the polymer. Changing the injection solvent composition will change retention times in a systematic manner. This can be explained with both chemical equilibria and conductivity models and may occur quite often in conventional EC. This effect does not appear to be discussed in the EC literature. Other Applications. We demonstrate a number of other simple separations in this section noting that these are synthetic mixtures and are considerably easier to separate than those which are present in difficult matrixes. Applications using CGEC where the sample matrix is complex are forthcoming from our laboratory. The baseline separation of a mixture of alkylphenones is shown in Figure 7. This mixture is composed of acetophenone, butyrophenone, hexanophenone, and octanophenone. The conditions are given in the figure caption. The retention times are slightly longer than those shown for the benzoates in Figure 2 because the polymer concentration is slightly higher (4.00%), and under these conditions, the electroosmotic flow velocity is slightly lower and retention is higher. This experiment is also conducted at the lower pH of 9.1, which has a slighly lower electroosmotic flow velocity than pH 11.3. Figure 8 shows the separation of a number of alkylbenzene compounds, specifically toluene, ethylbenzene, propylbenzene, and butylbenzene. These compounds show a slight degree of tailing and we have noticed this for a number of different aromatic compounds, which will be discussed below. Again, the resolution is fine and the separation is easy to perform. The separation of a number of oxidation inhibitors is shown in Figure 9. These compounds include hydroxyquinone, pmethoxyphenol, phenothiazine, and butylated hydroxytoluene. The separation is easily done and is competitive with other separation techniques such as HPLC and MEKC. We have compared nonionic surfactant separations (for example, Triton X-100) obtained by standard pump-driven reversedphase LC with the results from our polymer-based separations. Analytical Chemistry, Vol. 70, No. 23, December 1, 1998

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Figure 8. Separation of alkylbenzene compounds. Peaks: (1) toluene, (2) ethylbenzene, (3) propylbenzene, and (4) butylbenzene. Conditions: 1-kV injection for 15 s, 4.00% polymer retentive phase, run voltage 30 kV, solvent 40% acetonitrile at pH 9.1. The injection concentration of each compound is 1000 ppm.

Figure 9. Separation of oxidation inhibitor compounds. Peaks: (1) hydroxyquinone, (2) p-methoxyphenol, (3) phenothiazine, and (4) butylated hydroxytoluene. Conditions: 1-kV injection for 15 s, 4.03% polymer retentive phase, run voltage 30 kV, solvent 40% acetonitrile at pH 9.1. The injection concentration of each compound is 1000 ppm.

The two techniques give essentially the same elution pattern. This is interesting because surfactants such as Triton X-100 have a distribution in the PEO backbone length that is not resolved by reversed-phase LC at room temperature.39 However, the distribution is clearly visible by normal-phase chromatography.39 Because the surfactant separation using the polymer retentive phase is similar to the reversed-phase LC results and not the normal-phase LC results, the mechanism of separation in our CGEC experiments appears to be similar to reversed-phase HPLC. Hence, the charged polymer backbone apparently does not contribute significantly toward retention, as does the native silica surface used in normal-phase LC. Figure 10 shows the separation of a number of polycyclic aromatic hydrocarbons (PAHs) at the two pHs that have been used throughout this work. Resolution in both cases appears to (39) Rissler, K. J. Chromatogr., A 1996 742, 1-54.

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Figure 10. Separation of a PAH mixture at pHs 9.20 (top) and 11.5 (bottom). In both cases, there is 40% acetonitrile present. The polymer concentration is 3.99% for the 9.20 pH experiment and 4.01% for the pH 11.5 experiment. The 9.20 pH buffer is made with 10 mM sodium borate decahydrate, and the 11.5 pH buffer is made with 10 mM phosphate. In both cases, a 20-kV potential is placed across a 33-cm-length capillary (the electric field strength is 606 V cm-1) with 25 cm between injector and detector. Peaks: (1) benzene, (2) unknown, (3) naphthalene, (4) fluorene, (5) anthracene, (6) pyrene, (7) chrysene, (8) benzo[e]pyrene, and (9) benzo[ghi]perylene.

be excellent and very little difference is seen between the two experiments. Note that we are using a smaller length capillary (33 cm) for the PAH experiments as compared to the previous experiments (50 cm). We also note that an impurity was present in our mixtures that was not part of the original sample mixture, and this impurity elutes as peak 2 in the electrochromatograms. Some minor tailing is observed at higher retention, and a number of possible explanations for this exist. As is generally thought,21,32 tailing has its origins in the existence of different types of retentive sites of which there is a small population of sites where slow solute desorption occurs. The location of these sites is not clear in our experiments but may possibly be the silica capillary surface. However, the separations are fast and although not shown they are very reproducible. Occasionally, some noise is observed in these electrochromatograms and the origin is thought to be the detector rather than the capillary and the chemistry within the capillary. The source of the noise is difficult to locate and identify unambiguously. The detection wavelength used here is 200 nm, and this appears to provide the most sensitive wavelength. At 254 nm, the noise is reduced; however, the peak amplitudes are also reduced. Figure 11 shows the effect of field strength on the separation of the PAH mixture. It appears that the resolution is nearly constant between the 10-, 20-, and 30-kV experiments. This can be explained as follows. If experiments are conducted where axial broadening due to diffusion is the sole contribution to plate height, then one expects higher velocity experiments to reduce the plate height because of the relationship H ) 2D/v. However, nonequilibrium effects, when present, will increase H by an additional factor which is linear in velocity. If these two plate height terms approximately cancel, then plate height can be approximated as a constant. As can be seen from Figure 5, in the regions of highest velocity, the plate height does not change much with velocity.

Figure 11. Same PAH separation as in Figure 10 at pH 9.20 with three different operating voltages: 10, 20, and 30 kV. These result in electric fields of 303, 606, and 909 V cm-1, respectively. The capillary is the same as that used for Figure 10.

The zone resolution Rs can be equated to efficiency and thermodynamic parameters by the well-known equation33

Rs ) xN/16 ∆R/R

(2)

where Rs is resolution, N is the number of theoretical plates equal to L/H, and R is the retention ratio equal to 1/(k′ + 1). Equation 2 predicts that resolution will be invariant if the plate height (and hence N) and the phase equilibrium which affects R (the thermodynamic variable) are held constant. Another way to express this is to use the resolution ratio17 formed from eq 2 at constant R and ∆R:

Rs1/Rs2 ) xN1/N2

(3)

where the subscript indicates the corresponding experiment. Again, resolution is invariant if the number of plates is held constant under constant column thermodynamic conditions. This constancy of the number of plates is found in the experiments given in Figure 11; measurement of the plate count for the pyrene peak gives 34 200, 33 500, and 34 500 plates for the 10-, 20-, and 30-kV experiments, respectively. The extent to which this approximately constant plate height can be exploited for the highest possible resolution in the shortest time is currently being pursued through the use of shorter columns and higher field strengths. Movement of Polymer in the Capillary. In an effort to see whether the polymer moves in the capillary under the influence of the electric field, a number of experiments were tried. First, the capillary was filled with a 4% polymer solution. Water was then slowly injected into the capillary. Optical microscopy was used to see whether the polymer fluid/water interface could be detected as the water displaced the polymer. The interface could not be detected by standard optical microscopy or phase contrast microscopy. The polymer solution is very transparent, and two capillaries put side by side in the optical microscope, one filled with 4% polymer solution and the other filled with water, could not be differentiated. Hence optical monitoring of the polymer solution would not be able to detect its movement.

Next, a number of separations were tried where the experiment was run without polymer in the buffer vials (both injection and detection sides) and only buffer was present in the vials. The polymer was initially pumped into the capillary in these experiments to effect separation. In these experiments, the benzoate mixture is used as a test solute mixture and the capillary is 50 cm long with a 30-kV potential difference. In this configuration, typically one experiment with full separation can be run which has nearly the same resolution as those experiments where polymer is in both vials. Subsequent experiments without polymer in the buffer vials gave only one peak. When the polymer is present in the buffers, reproducible peaks are able to be had for at least 10 experiments without reloading the polymer. This suggests that the polymer does move slowly in the capillary during the experiment but is replenished in the capillary by the polymer in one of the buffer vials. It is difficult to judge which direction the polymer moves. The electroosmosis is from anode to cathode; i.e., the polymer counterions electrophorese down the capillary from injection to detection side.The polymer, being negatively charged, most likely electromigrates in the opposite direction, consistent with the large negative charge. However, since the polymer used in these experiments has colloidal dimensions with a radius of gyration in excess of 80 nm, the electrophoresis of polymer takes place over a time scale much slower than the electrophoresis of the counterion which gives fluid flow. This may appear to be a problem if a detector like a mass spectrometer is to be used. However, the use of dialysis membranes on one or both ends of the capillary is not out of the question. We are pursuing this presently as an option for this type of analysis and to see whether only one side of the capillary needs to have a containment membrane. Advantages and Disadvantages of CGEC. The present study has emphasized that both speed and low zone broadening are distinct advantages of CGEC, as shown through the data presented here. In addition, the retentive phase is renewable, a unique feature for bonded-phase chromatography but well acknowledged in MEKC and in CGE. There are disadvantages to this form of the CGEC technique as emphasized earlier in that sample capacity is small and this places an additional burden on the detectability of solute. Perhaps the most difficult problem is polymer compatibility with the solvent; this effect will now be discussed in some detail. The polyelectrolytes with grafted hydrophobes have a limited solubility range for the acetonitrile/water mixtures used in these studies. When the acetonitrile to water ratio is smaller than 30:70 at a gel concentration of 4%, the polymer solution getscloudy and the viscosity of the solution increases dramatically, suggesting that phase separation is taking place. However, the acetonitrile concentration can be brought lower when smaller gel concentrations are used. Acetonitrile concentrations higher than 50% are difficult because the buffer salts precipitate at this higher concentration. Below the acetonitrile to water concentration ratio of 30:70 at a gel concentration of 4%, experiments show that the capillary cannot be loaded without great difficulty and detection is noisy. In addition, a sensitivity loss is noted because of the large amount of scattering in the detector region of the capillary. Utilization of Analytical Chemistry, Vol. 70, No. 23, December 1, 1998

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other aqueous solvent mixtures with methanol and with THF appear to either reduce electroosmotic flow to a large extent or to render the retentive phase insoluble. Another disadvantage with any EC technique and of particular importance here is the variability in retention times which occur due to the difference in conductivity between the injection plug and carrier buffer. This effect is known to occur in CE for some highly charged samples; in the CE case, the sample is charged and conducts to a much higher degree than the buffer. This is in contrast to EC and CGEC where the carrier conducts but the sample does not. As mentioned previously, this effect does not appear to be discussed in the EC literature, however, we have noted in our limited study of system peaks that small changes in the injection buffer composition can affect retention times by a few percent. This is an inconvenience and must be noted to occur for the analyst to effectively utilize these techniques. The pH range we have used in these studies varies from pH 9.1 to 11.3 and is controlled by a simple selection of buffer. Again, pH is chosen mostly on a polymer solubility basis but is also chosen for performance and for sample compatability. The methacrylic acid backbone is nearly completely dissociated above pH 8, but solubility of the polymer falls off as the pH is decreased. In the case of pH 11.3, the fused silica capillaries have a shorter lifetime and require replacement every few days. Our initial experiments were conducted at this very high pH, but it was found that performance did not degrade by running at pH 9.1. The stability of some of the solutes, however, becomes an issue at the higher pH. It does not appear possible to run this experiment at a pH lower than 8, due to polymer solubility. Further experiments need to be conducted to assess the performance of this style of separation with charged compounds. It has been previously demonstrated that chromatographic retention can sometimes aid in the electrophoretic separation of similar compounds.40 CGEC Contrasted with Packed Bed EC. Although much discussion has taken place on conditions where convective flow occurs in the pores of packed bed particles,41,42 it is quite probable that for particles with small pore sizes (e.g., dp < 200 Å, where dp is the pore size), flow does not occur in pores to any appreciable extent when pressure-driven flow is used. Using theory from ref 41, it can be shown that the ratio 〈νp〉/〈ν〉 where 〈νp〉 is the average fluid velocity in a pore and 〈ν〉 is the average bed fluid velocity, is most dominantly determined by the ratio dp/d, where d is the particle diameter. The diameter ratio is ≈4 × 10-3 for dp ) 200 Å and d ) 5 µm, indicating that convective flow in pores is not important; hence diffusion in to and out of the particle is the dominant retentive phase mass transport mechanism. For the case of packed bed EC, electroosmotic flow should be able to take place inside the pore structure of the particle since small pore sizes do not limit the flow velocity, as in pressuredriven flow. In this regard, small-pore convective transport may occur to some extent in packed bed EC if the electric field vector is oriented parallel to the pore. For a simple capillary model of a particle pore structure, it would appear that not all of the pores would be active toward electroosmotic flow; i.e. pores that are (40) Schure, M. R.; Murphy, R. E. J. Electrophor. 1995, 16, 2074-2085. (41) Afeyan, N. B.; Gordon, N. F.; Mazsaroff, I.; Varady, L.; Fulton, S. P.; Yang, Y. B.; Regnier, F. E. J. Chromatogr. 1990, 519, 1-29. (42) Liapis, A. I.; McCoy, M. A. J. Chromatogr. 1992, 599, 87-104.

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perpendicular to the electric field vector will have no electroosmotic flow. The most probable case is where the pore is at an angle to the field. In this case, we expect some electroosmotic flow will take place in the pore but not at the velocity where the pore length is parallel to the electric field vector. However, the presence of flow in a complex pore geometry will modify the ion distribution near the double layer, which suggests that an accurate calculation of the flow inside an aggregate of silica microspheres is exceedingly complex. Other papers have dealt with the calculation of flow in a porous floc of particles;43-46 however, these are mean-field treatments and do not discuss the necessary microhydrodynamics needed to determine the detailed nature of the flow inside the particle. Hence, zone broadening in EC with a packed bed of porous particles may have less contribution from retentive-phase mass transport than in the case of pressure-driven flow. In the CGEC experiment, the retentive-phase mass transport should be very small because the distance between the adjacent retentive and convective sites is on the order of tens of angstroms. This is observed experimentally in the low magnitude of the C term from the plate height study. However, the reduced pore size in the polymer may cause a parabolic-like velocity profile as the double layers in the pore overlap,28 which is similar to the velocity profile from pressure-driven flow. The larger pore length scales found in packed bed particles may preserve the flatness28 of the velocity profile, which is known to give better performance in channels of uniform geometry.6 This point needs further research and may be probed experimentally in the future. Another difference between CGEC and packed bed EC is the solvent compatibility requirements. In CGEC, the support material is a polymer chain and the polymer chain must be soluble in the carrier solution for ease of use. This places a more limited solvent range on the CGEC experiment as opposed to the packed bed configuration where solubility is usually not an issue for the support. Also, solid particles based on inorganic materials used in packed bed columns are not susceptible to swelling or collapse as is a polymer chain. From a chemical design point of view, the difficult problem in CGEC using a grafted hydrophobe polymer architecture is designing a phase that has a high hydrophobic character and maintains reasonably high solution solubility. One other aspect of packed bed EC using bonded phases is the desirability of shielding of the electroosmotic sites by the retentive phase. With a chemically modified surface on a solid particle where the solid particle surface provides the electroosmotic flow, there is a certain degree of surface shielding of the electroosmotic sites from the solute because of the grafted chains. This is very desirable because the interaction of the solute with the electroosmotic flow generation site is reduced, as compared with CGEC where, because of the solubility problem, one cannot shield the electroosmotic sites with a significant amount of retentive material. It is possible that the interaction of solute with electroosmotic flow surface sites can modify the flow in the vicinity of the solute zone as a function of concentration through transient (43) Kozak, M. W.; Davis, E. J. J. Colloid Interface Sci. 1989, 127, 497-510. (44) Miller, N. P.; Berg, J. C.; O’Brien, R. W. J. Colloid Interface Sci. 1992, 153, 237-243. (45) O’Brien, R. W. J. Colloid Interface Sci. 1995, 171, 495-504. (46) Coelho, D.; Shapiro, M.; Thovert, J. F.; Adler, P. M. J. Colloid Interface Sci. 1996, 181, 169-190.

complex formation, leading to possible non-Gaussian zone generation. These effects are reduced in packed bed EC because of the retentive site shielding mentioned above. The future of EC and CGEC depends on a number of different factors besides the raw performance that these systems appear to be capable of delivering. As the ease of use aspect increases in importance, with further use of these systems, we may see an increase in the emphasis on replaceable media because of the small pore sizes, and hence possible limited lifetimes of these types of separation media. This becomes extremely important for the adaptation of these technologies toward routine use especially when complex matrixes are present.

N h bh

average number of monomer units between hydrophobe grafting sites

N h gh

average number of grafted hydrophobe segments per chain

Nt

number of monomer units per polymer in the backbone

R

retention ratio

Rg

radius of gyration

Rs

resolution

tr

retention time

t0

passage time of an unretained zone

Vp

volume of spherical polymer segment

Vo

effective volume of a packed polymeric spherical segment

ACKNOWLEDGMENT 〈ν〉

average velocity

〈νp〉

average pore velocity



fraction of total volume contained external to the surface

b

fraction of interstitial volume

constants in the van Deemter equation

p

fraction of pore volume

Am

surface area of packing in (m2 g-1)

η

viscosity

Cp

concentration of polymer in solution as a weight percent

η0

viscosity of the solution without polymer

F

density of bulk material (in g mL-1)

Cv

concentration of bonded phase (in µmol/mL)

Fb

bonding density (in µmol/m2)

D

diffusion coefficient

Fs

superficial density of material (in g mL-1)

d

column diameter, particle diameter

l

pore size scaling exponent

dp

pore diameter in a chromatographic particle

σ

standard deviation of a Gaussian zone

f

geometrical packing factor

ξ

pore mesh size in entangled polymer

H

total plate height

k′

capacity factor

L

column length from injector to detector

Received for review July 6, 1998. Accepted September 20, 1998.

N

number of theoretical plates

AC980719D

We thank Carl Hemenway and Richard Ketz of the Rohm and Haas Rheology Research group for obtaining the viscosity data used in this and other studies. SYMBOLS A, B, C

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