Porous and Nonporous Particles in Packed Capillary Column

Sep 23, 1999 - The contributions of mass-transfer resistance (Cstag) to the plate height from the stagnant mobile phase were compared for liquid ...
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Anal. Chem. 1999, 71, 5084-5092

Porous and Nonporous Particles in Packed Capillary Column Solvating Gas Chromatography Naijun Wu, Qinglin Tang, Yi Shen, and Milton L. Lee*

Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah 84602-5700

In this paper, the efficiencies and peak capacities of columns packed with nonporous and porous particles were investigated under typical solvating gas chromatography (SGC) conditions using a carbon dioxide mobile phase. The contributions of mass-transfer resistance (Cstag) to the plate height from the stagnant mobile phase were compared for liquid chromatography (LC), supercritical fluid chromatography (SFC), and SGC using 5-µm nonporous and porous particles. The results show that the contribution of the Cstag term to the total mobile-phase mass-transfer resistance for porous particles decreased markedly from LC to SFC to SGC. In SGC, mass-transfer resistance in the stationary phase and longitudinal diffusion are more significant. The total mass-transfer terms for nonporous silica (5 and 10 µm) encapsulated with SE54 (e.g., 1% w/w loading) were 30-40% higher than those for porous silica (5 µm, 120 Å, and 10 µm, 80 Å) encapsulated with SE-54 (e.g., 10% w/w loading). Polymerencapsulated porous particles are more suitable for fast SGC than nonporous particles at the same linear velocity although higher column inlet pressure is required. Peak capacities of columns packed with nonporous particles were lower compared to columns packed with porous particles when the same linear velocity was used. Highspeed separations can be achieved using very short columns packed with small porous particles in SGC. The overall goal of analytical chromatography is to achieve sufficient resolution of analytes of interest within the shortest possible time. One approach to reaching this goal in packed column chromatography is to improve the structural characteristics of the stationary phase, such as reducing the mass-transfer resistance in the stagnant mobile phase,1,2 using a thin stationaryphase film to reduce the mass-transfer resistance in the stationary phase3 and using small particles to reduce eddy diffusion and mass-transfer resistance in the mobile phase.4 A significant amount of research has recently been carried out using nonporous particles as stationary-phase supports in liquid chromatography (LC).1,2,4-6 Small nonporous particles have been successfully used (1) Chen, H.; Horva´th, Cs. J. Chromatogr., A 1995, 705, 3-20. (2) Banks, J. F.; Gulcicek, E. E. Anal. Chem. 1997, 69, 3973-3978. (3) Barry, E. F. In Modern Practice of Gas Chromatography; Grob, R. L., Ed.; 3rd ed.; John Wiley & Sons: New York, 1995. (4) Barder, T. J.; Wohlman, P. J.; Thrall, C.; DuBois, P. D. LC-GC 1997, 15, 918-926. (5) Hanson, M.; Unger, K. K. J. Chromatogr. 1990, 517, 269-284.

5084 Analytical Chemistry, Vol. 71, No. 22, November 15, 1999

for fast separations of a variety of samples, including biopolymers such as proteins and peptides.7,8 However, the applicability of nonporous particles to fast separations in packed column supercritical fluid chromatography (SFC) and gas chromatography (GC) has not been investigated until now. Recently, we found that packed capillary column solvating gas chromatography (SGC) is an alternative to SFC and LC for high speed 9-11 and high efficiency.12 The mobile phase in the most typical form of SGC is a supercritical fluid at the column inlet and a gas at the outlet. The mobile phase gradually changes from a supercritical fluid to a gas within the column as the pressure drops to atmospheric pressure at the end of the column. In this study, we first compared the contributions of the stagnant mobilephase mass-transfer resistance to the plate heights for LC, SFC and SGC, using 5-µm nonporous and porous particles. Second, we investigated the column efficiency obtained using polymerencapsulated nonporous particles under practical SGC conditions, and the results were compared with those obtained when porous particles were used. Finally, we compared the peak capacities of the columns packed with these two types of particles using a newly developed peak capacity equation13 and demonstrated the applicability of nonporous and porous particles to fast separations in SGC. THEORY Band broadening in a uniform packed column arises from several independent kinetic processes. In LC, these processes can be summarized using the general van Deemter equation:14

h ) A + B/u + Cu

(1)

where h is the reduced plate height, u is the linear velocity, and A, B, and C are coefficients that represent a particular column, solute, and set of elution conditions. The A term reflects the contribution to the plate height attributable to inhomogeneous flow. B/u is the result of longitudinal molecular diffusion along (6) Hanson, M.; Unger, K. K. LC-GC 1997, 15, 170-178. (7) Mao, Q.; Prince, I. G.; Hearn, M. T. W. J. Chromatogr., A 1995, 691, 273283. (8) Lee, W.-C.; Chuang, C.-Y. J. Chromatogr., A 1996, 721, 31-39. (9) Shen, Y.; Lee, M. L. J. Chromatogr., A 1997, 778, 31-42. (10) Shen, Y.; Lee, M. L. Anal. Chem. 1998, 70, 737-742. (11) Wu, N.; Shen, Y.; Lee, M. L. Chromatographia 1998, 47, 673-678. (12) Shen, Y.; Lee, M. L. Anal. Chem. 1997, 69, 2541-2549. (13) Shen, Y.; Yang, J. Y.; Lee, M. L. Anal. Chem. 1997, 69, 628-635. (14) van Deemter, J. J.; Zuiderweg, F. J.; Klinkenberg, A. Chem. Eng. Sci. 1956, 5, 271-289. 10.1021/ac990650p CCC: $18.00

© 1999 American Chemical Society Published on Web 09/23/1999

the axis of the column. The Cu term represents the contribution from slow mass transfer. Other modifications of this equation were reported by Horva´th and Lin,15 Giddings,16 and Done and Knox.17 For fast separations, the mass-transfer resistance term is most important since high linear velocities are used. For unretained solutes, the only difference between nonporous and porous particles is that nonporous particles eliminate the mass-transfer resistance from the stagnant mobile phase because there are no pores in the nonporous packing. Among the various equations, only the Horva´th-Lin equation describes the contribution from the stagnant mobile phase to the resistance to mass-transfer term for unretained solutes:18

Cstag ) θk0dp2/30Dm(1 + k0)2

(2)

where θ is the tortuosity factor for the porous particles, which is related to the ratio of solute diameter to pore diameter,18 Dm is the diffusion coefficient of the solute in the mobile phase, k0 is the ratio of the intraparticle void space to the interstitial void space in the column, and dp is the particle diameter. The value of k0 is typically between 0.5 and 0.8 for most porous particles.19 It can be seen from eq 2 that the resistance to mass transfer from the stagnant mobile phase is proportional to the square of the particle diameter and inversely proportional to the diffusion coefficient of the solute in the mobile phase. Decreasing the particle size and increasing the diffusion coefficient can effectively improve the mass transfer of solutes in the stagnant mobile phase. In other words, when small particles or mobile phases of low density are used, such as enhanced fluids or even gases, the contribution to mass-transfer resistance from the stagnant mobile phase will become less significant. When a compressible mobile phase is used in chromatography, the average diffusion coefficient of a solute in the mobile phase depends on the average pressure of the mobile phase along the column. The temporal or spatial average pressure of the mobile phase in the packed column is related to the ratio of the inlet pressure to the outlet pressure of the column. Therefore, for GC and SFC conditions, the general van Deemter equation must be modified by considering the compressibility of the mobile phase. Based on the experimental relationship between pressure and diffusion coefficient for supercritical fluids, the relationship between pressure drop and linear velocity for packed columns, and the van Deemter equation, the column efficiency of packed column SFC for unretained solutes can be derived:13

h ) A + B′/u1.5 + C ′u1.5

(3)

where A, B′, and C ′ are constants independent of the mobilephase linear velocity for a particular column, solute, and set of elution conditions. It can be seen that, in packed column SFC, the plate height is a function of the mobile-phase linear velocity to the 1.5 order. (15) Horva´th, Cs.; Lin, H.-J. J. Chromatogr. 1976, 126, 401-420. (16) Giddings, J. C. J. Chromatogr. 1961, 5, 46-60. (17) Done, J. N.; Knox, J. H. J. Chromatogr. Sci. 1972, 10, 606-612. (18) Brenner, H.; Gaydos, L. J. J. Colloid Interface Sci. 1977, 58, 312-356. (19) Horva´th, Cs.; Lin, H.-J. J. Chromatogr. 1978, 149, 43-70.

No theoretical relationships between plate height and linear velocity have been found for packed capillary SGC. When a typical mobile phase, carbon dioxide, is used in SGC, the flow properties of carbon dioxide are very similar to those of a gas at temperatures higher than 90 °C and pressures lower than 250 atm.20-22 Therefore, the modified van Deemter equation for packed capillary GC for unretained solutes13 can be used for packed capillary SGC:

h ) A + B′′/u2 +C ′′u2

(4)

where B′′ and C ′′ are constants independent of the linear velocity. This equation was derived in a manner similar to that for eq 3.13 It can be seen from eq 4 that, in packed column SGC, the plate height is a function of the square of the mobile-phase linear velocity. Using the equations discussed above and for typical chromatographic operating conditions, the mass-transfer resistance in the mobile phase can be compared for columns packed with porous and nonporous particles in LC, SFC, and SGC. The peak capacity is the most useful measurement of the separation power of a chromatographic column as it gives the number of peaks separable with a resolution of unity within a specific time interval. Giddings23 developed a number of mathematical expressions of the peak capacity for packed columns, based on the assumption that the number of theoretical plates produced by the column is the same for all solutes. However, for most columns, column efficiency greatly depends on solute retention.24,25 Recently, Shen and Lee26 introduced a more universal peak capacity equation based on the fact that the peak width at half-height (w1/2) linearly increases with increasing retention time t under isothermal and isobaric conditions:

w1/2 ) at - b

(5)

The constants a and b in eq 5 can be determined by experiment using a series of homologous compounds. In most situations, the constant b in eq 5 is positive, and thus, it is more convenient to use this form of the equation than to use w1/2 ) at + b, although there is no substantial difference between the two equations.26 Thus, peak capacity can be calculated once a and b constants in eq 5 are known:

n)1+

x5.54 atn - b ln 4a at1 - b

(6)

where n is the peak capacity and tn and t1 are the retention times of the nth and first peaks, respectively. The constant a equals (5.54/N∞)1/2, where N∞ is the theoretical plate number when the retention time approaches infinity. The constant b represents the (20) Shen, Y.; Lee, M. L. Chromatographia 1997, 46, 537-544. (21) Liong, K. K.; Wells, P. A.; Foster, N. R. J. Supercrit. Fluids 1991, 4, 91108. (22) Balenovic, Z.; Myers, M..N.; Giddings, J. C. J. Chem. Phys. 1970, 52, 915922. (23) Giddings, J. C. Anal. Chem. 1967, 39, 1027-1028. (24) Krupcˇ´ık, J.; Garaj, J.; CÄ ella´r, P.; Guiochon, G. J. Chromatogr. 1984, 312, 1-10. (25) MacNair, J. E.; Lewis, K. C.; Jorgenson, J. W. Anal. Chem. 1997, 69, 983989. (26) Shen, Y.; Lee, M. L. Anal. Chem. 1998, 70, 3853-3856.

Analytical Chemistry, Vol. 71, No. 22, November 15, 1999

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influence of retention factor on N. The larger the b value, the more significant the column efficiency difference is for different retained solutes. In this study, we used the dead time t0 as t1. Replacing a and t1 terms with (5.54/N∞)1/2 and t0, respectively, eq 6 can be expressed as

n)1+

xN∞ ln 4

[

tn - t 0

t0 - bxN∞/5.54

+1

]

(7)

It can obviously be seen from eq 7 that, within a given separation time tn, the peak capacity increases with increasing column efficiency and constant b or with decreasing dead time of the column. In this paper, we compare the effects of these factors on the peak capacities for columns packed with nonporous and porous particles. EXPERIMENTAL SECTION Materials. Spherical nonporous particles of 5- and 10-µm diameter were purchased from Jones Chromatography (Mid Glamorgan, U.K.). Spherical porous silica (5 µm, 120 Å, and 10 µm, 80 Å) particles were purchased from Alltech (Deerfield, IL). Spherical nonporous ODS particles (3 µm) were obtained from Micra Scientific (Northbrook, IL). Spherical porous ODS (3 µm, 80 Å) particles were purchased from Phase Separations (Norwalk, CT). Poly(methylhydrosiloxane) (PS-118; United Chemicals, Bristol, PA) was used to deactivate the silica particles. SE-54 (5% diphenyl-94% dimethyl-1% vinylpolysiloxane) was purchased from Aldrich (Milwaukee, WI). Fused-silica capillary tubing was purchased from Polymicro Technologies (Phoenix, AZ). HPLC grade acetonitrile was purchased from Fisher Scientific (Fair Lawn, NJ). All other chemicals used were purchased from Alltech (Milwaukee, WI) or Sigma (St. Louis, MO). Preparation of Packed Capillary Columns. SE-54 is a crosslinkable methylpolysiloxane stationary phase containing a low percentage of phenyl substitution, which is frequently used for gas chromatography.3 SE-54-encapsulated porous particles were prepared by first deactivating the particles using poly(methylhydrosiloxane) (PS-118) to remove the most active silanol groups on the silica particle surface, followed by coating and cross-linking of an SE-54 film on the deactivated particles. The detailed procedure can be found in the literature.27 To avoid sticking together of the nonporous particles, a two-step cross-linking method was used to prepare uniform stationary-phase films; that is, an SE-54 film was coated and cross-linked twice, with the second coating yielding a thinner film than the first. The porous particles were packed into the capillary columns using a CO2 slurry method as previously described.28 The nonporous particles were packed using a methanol-CO2 slurry method. We found that the nonporous particles were suspended better in the methanol-CO2 mixture than in pure CO2 because they have a higher density than porous particles. SGC and SFC Experiments. SFC and SGC experiments were carried out using a Lee Scientific model 501 SFC instrument (Dionex, Salt Lake Division, Salt Lake City, UT) using SFC grade CO2 (Scott Specialty Gases, Plumsteadville, PA). Column connections were made using zero dead volume unions (Valco Instruments, Houston, TX). A manual liquid injector (Valco Instruments) with a rotor volume of 0.2 µL was used for introduction of samples. 5086

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For SFC, a tapered restrictor was made on a 50 µm-i.d. fusedsilica capillary connected to the packed column outlet. For SGC, the restrictor was eliminated, and a 10 cm × 50 µm i.d. length of capillary tubing was used for the connection to the detector. Fusedsilica capillaries of 10 and 15 cm (15 µm i.d.) in length were used as split lines for split injection in SGC and SFC, respectively. For high-speed SGC separations, a 10 cm × 20 µm i.d. fused-silica capillary was used as a split line. Detection was accomplished using an FID. The dead time (t0) of columns was measured using methane. LC Experiments. A liquid chromatography pump (Varian 8500, Walnut Creek, CA) was used for the LC experiments. The packed capillary column was directly connected to a manual liquid injector valve (Valco, 60-nL sample loop). Acetonitrile was used as the mobile phase, and nitromethane was used as an unretained solute to mark the linear velocity and to determine the column efficiency. Detection was carried out using a UV absorption detector (UV-vis Spectra 100, Thermo Separation Products, San Jose, CA). Data Analysis. A microcomputer equipped with Systat 8.0 (SPSS, Chicago, IL) was used for least-squares analysis of the experimental data. RESULTS AND DISCUSSION For silica-based particles, the silica surface chemistry is mainly determined by silanol groups on the particle surface.29 Anspach et al.30 determined the silanol group concentration on the surface of 2.1-µm nonporous silica particles using 1H NMR spectroscopy and found this value to be ∼8 µmol m-2. Zhuravlev and Kiselev31 investigated a series of porous silica particles that differed widely in origin and porosity and found that the mean silanol group concentration on the surface ranged from 7.0 to 9.5 µmol m-2, essentially independent of the specific area of the particles. Therefore, we believe that the surface chemistry for nonporous particles is similar enough to that for porous particles that we can make reasonable comparisons. Furthermore, when we compared porous and nonporous particles in SGC, both types of particles were deactivated and cross-linked with poly(methylhydrosiloxane) and SE-54 stationary phase. Thus, the surface chemistry for these two types of cross-linked particles should be very similar. Column Efficiency for Unretained Solutes. Since fast separations are emphasized in this study, column efficiency will be discussed in terms of mass-transfer resistance. To estimate the contribution to plate height from the stagnant mobile phase, the contribution of mass-transfer resistance from the stationary phase must be eliminated; thus, unretained solutes were used. Figure 1 shows experimental results of column efficiency as a function of mobile-phase linear velocity under LC, SFC, and SGC conditions using capillary columns packed with 5-µm porous and (27) Shen, Y.; Malik, A.; Li, W.; Lee, M. L. J. Chromatogr., A 1995, 707, 303310. (28) Malik, A.; Li, W.; Lee, M. L. J. Microcolumn Sep. 1993, 5, 361-367. (29) Unger, K. K. Porous Silica; Elsevier: Amsterdam, The Netherlands, 1979; Chapter 3. (30) Anspach, B.; Unger, K. K.; Davies, J.; Hearn, T. W. J. Chromatogr. 1988, 457, 195-204. (31) Zhuravlev, L. T.; Kiselev, A. V. In Proceedings of the IUPAC International Symposium on Surface Area Determinations; Everett D. H., Ottewill, R. H., Eds.; Butterworths: London, 1970; p 155.

Table 1. Mass-Transfer Resistance in the Mobile Phase for LC, SFC, and SGCa LC (cm-1 s)

SFC (cm-1.5 s1.5)

SGC (cm-2 s2)

nonporous particles (NP) 12.74 ( 1.37b 5.26 ( 0.70 1.65 ( 0.19 porous particles (P) 24.50 ( 2.13 6.94 ( 0.47 1.85 ( 0.21 (Cp - CNP)/CP × 100% 48.0 24.2 10.8 a Conditions: same as in Figure 1. b The confidence intervals were calculated at 95% confidence level.

Figure 1. Van Deemter curves for packed capillary LC, SFC, and SGC. Conditions: (A) LC, 55 cm × 250 µm i.d. fused-silica capillary columns packed with 5-µm porous (120 Å) and nonporous silica particles, nitromethane test solute, 25 °C, UV detector (214 nm); (B) SFC, 75 cm × 250 µm i.d. fused-silica capillary columns packed with 5-µm porous (120 Å) silica deactivated with poly(methylhydrosiloxane) and cross-linked with SE-54 (10% w/w) and nonporous silica deactivated with poly(methylhydrosiloxane) and cross-linked with SE54 (1.5% w/w), 45 °C, 230 atm, carbon dioxide mobile phase, methane test solute, FID; (C) SGC, 120 °C; other conditions are the same as for SFC. Solid lines represent regression analysis.

nonporous particles. It can be seen from the figure that, at high linear velocities, the columns packed with nonporous particles produced small plate heights. The difference in plate height between nonporous and porous particles, however, is less significant from LC to SFC to SGC at high linear velocities. The experimental data shown in Figure 1 were analyzed using least-squares analysis according to eqs 1, 3, and 4 for LC, SFC,

and SGC, respectively. The R2 values for all equations were greater than 0.98. This shows that the modified van Deemter equations (3 and 4) are suitable for SFC and SGC, respectively, and the classical van Deemter equation (1) fits well with the LC data. The calculated mass-transfer resistance terms (Cm) in the mobile phase are listed in Table 1. If the mass-transfer resistance from the stagnant mobile phase is considered to be the only difference between nonporous and porous particles, the difference (CP CNP) in the Cm term between nonporous and porous particles in Table 1 can be used as an estimate of the contribution of the masstransfer resistance (Cstag) from the stagnant mobile phase to the plate height. However, direct comparison of mass-transfer resistance terms for LC, SFC, and SGC is not reasonable because the coefficients for the Cm terms in Table 1 have different units. Thus, the relative percentages of the differences (CP - CNP ≈ Cstag) in mass-transfer resistance terms for porous and nonporous particles compared to the total mass-transfer resistance term (CP) were used for comparison of the contributions of stagnant mobile-phase resistance to plate height for the different forms of chromatography. The results in Table 1 show that the percentage of the Cstag term in the total mobile-phase mass-transfer resistance for porous particles decreased markedly from LC to SFC to SGC. The main reason for this can be ascribed to the fact that the viscosity of the mobile phase decreases and the diffusivity increases greatly from LC to SFC to SGC. Equation 2 shows that mass-transfer resistance from the stagnant mobile phase (Cstag) decreases with an increase in diffusion of the mobile phase. The contribution of longitudinal diffusion to the total plate height is significant in SGC, which is readily explained by the high diffusion coefficient of the mobile phase under typical SGC conditions. The B term for the column packed with nonporous particles in SGC is 16.63 cm2 s-2, which is 54% higher than that (7.66 cm2 s-2) obtained from the column packed with porous particles. This can be explained by the high permeability of the column packed with nonporous particles. Producing the same linear velocity requires lower inlet column pressure for the column packed with nonporous particles than for the column packed with porous particles because of its high permeability, as shown in Figure 2. At the same linear velocity, the column packed with nonporous particles operates with a mobile phase of lower viscosity and density, which leads to a higher B term. It should be noted that the pressure versus linear velocity curves are not linear when pressures are higher than 200 atm. This can be explained by the fact that the viscosity of carbon dioxide increases with increasing pressure more significantly at higher pressures. Another possible reason for the higher B term is that the constriction and tortuosity factors for columns packed with Analytical Chemistry, Vol. 71, No. 22, November 15, 1999

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Figure 2. Relationship between pressure drop and linear velocity for nonporous and porous particles in SGC. Conditions: 5-µm particles in 55-cm columns; 10-µm particles in 100-cm columns; other conditions are the same as in Table 3.

nonporous particles are favorable for free longitudinal molecular diffusion because nonporous particles have a solid sphere structure and a smooth surface.32 In LC, nonporous particles are more favorable than porous particles for the separation of high-molecular-weight compounds such as peptides and proteins.7,8 These analytes have low diffusion coefficients; therefore, they have negligible longitudinal diffusion terms and large mass-transfer resistance terms from the mobile phase. In SGC or GC, however, compounds that are separated are relatively volatile and, thus, readily diffuse in the “stagnant” mobile phase. In addition, longitudinal diffusion is more significant for nonporous particles. Considering these factors that affect the diffusion of solutes in the mobile phase, nonporous particles do not have considerable advantages over porous particles in SGC. Column Efficiency for Retained Solutes. For practical applications, the contribution of mass-transfer resistance to plate height from the stationary phase should be considered. To compare the relative contributions of mass-transfer resistance from the mobile phase and the stationary phase in SGC, plots of plate height versus linear velocity were constructed using data from methane and octane as unretained and retained solutes, respectively, as illustrated in Figure 3. It can be seen that the slope of the mass-transfer part of the plot for octane is much greater than that obtained for methane. This result suggests that mass-transfer resistance in the stationary phase is proportionally more significant in packed capillary column SGC, while the situation is reversed in open tubular column GC. The main reason for this is that the mass-transfer distance in the mobile phase is very short since microparticles are used as packing materials. Figure 3 also shows that the van Deemter plot for the retained solute (octane) exhibits much less longitudinal diffusion than for the unretained solute (methane). The experimental relationships of plate height and linear velocity were compared for columns packed with 5-µm nonporous and porous particles deactivated with PS-118 and crosslinked with SE-54, as shown in Figure 4. In contrast to the result in Figure 1C where unretained methane is used as test solute, (32) Giddings, J. C. Dynamics of Chromatography Part I. Principles and Theory; Marcel Dekker: New York, 1965.

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Figure 3. Plots of plate height versus linear velocity for unretained and retained solutes in SGC. Conditions are the same as in Figure 1C.

Figure 4. Plots of plate height versus linear velocity for columns packed with 5-µm nonporous and porous particles in SGC. Conditions are the same as in Figure 1C, except for octane test solute.

for retained octane, the slope of the plot from the column packed with nonporous particles is greater than that found for the column packed with porous particles. In packed column GC, the contribution of mass-transfer resistance to plate height can be expressed as14,33

C ) C m + Cs )

2 df2 (1 + 6k + 11k2) dp 2k f + f2 1 24(1 + k)2 Dm 3(1 + k)2 Ds

(8)

where Cs is the mass-transfer resistance in the stationary phase, k is the retention factor, df is the thickness of the stationary-phase film, Ds is the diffusion coefficient of a solute in the stationary phase, and f1 and f2 are calibration factors related to the column inlet pressure. It can be seen from eq 8 that the Cs term is proportional to the square of the film thickness of the stationary phase. Thus, in packed column GC, the thickness of the stationaryphase film has a considerable effect on column efficiency. (33) Katz, E. D.; Ogan, K. Scott, R. P. W. In The Science of Chromatography; Bruner, F., Ed.; Elsevier: Amsterdam, 1985; p 403.

Table 2. Total Mass-Transfer Resistance (Ctotal) for Nonporous and Porous Particles in SGC particle diam (µm)

particle type and polymer loading

Ctotal (cm-1 s)

[CNP - CP]/ CNP × 100%

5a

NPS (1.5% SE-54) PS (10% SE-54) NPS (1% SE-54) PS (10% SE-54)

8.62 ( 0.52c 5.14 ( 0.71 5.98 ( 0.74 4.02 ( 0.32

40.3

10b

32.8

a Conditions: 75 cm × 250 µm i.d. fused-silica capillary columns packed with 5-µm porous silica (120 Å) deactivated with poly(methylhydrosiloxane) and cross-linked with SE-54 (10% w/w) and nonporous particles deactivated with poly(methylhydrosiloxane) and cross-linked with SE-54 (1.5% w/w), 120 °C, carbon dioxide mobile phase, methane test solute, and FID. b The conditions are the same as for 5-µm, except for 100-cm columns packed with 10-µm porous (80 Å) and nonporous particles. c The confidence intervals were calculated at 95% confidence level.

Figure 5. Comparison of k/(k + 1)2 values between porous and nonporous particles. Conditions are the same as in Figure 4.

In SFC and GC, polymers such as SE-54 are usually coated or cross-linked on the silica particle surface to provide satisfactory inertness, thermal stability, and selectivity. Typically, polymer loadings for nonporous and porous particles are near 1-2 and 10-15% (w/w), respectively, to produce suitable retention and inertness (by covering silanol groups).34-36 When the polymer loading is more than 3% on nonporous particles, they readily stick together and prevent uniformity in the packed column bed.34 On the other hand, if the polymer loading on the nonporous particles (3-10 µm) is less than 0.05%, the retention is too low to be practical for the separation of most compounds. In this study, we used 1-1.5 and 10% polymer loadings for nonporous and porous particles, respectively. The ratio of film thicknesses of nonporous (dNP ) particles to porous (dP) particles of the same diameter can be estimated from the respective surface areas (A) and polymer loadings (W):

dNP f dPf

≈

NP Wloading /ANP P Wloading /AP

≈

1%/2m2g-1 5 ) 2 -1 1 10%/100m g

(9)

It can be seen that the average film thickness for a 1% loading on nonporous particles (5-10 µm) is ∼5 times that for a 10% loading on nonporous particles. This is a very conservative estimate because the surface area for 5-10-µm nonporous particles is less than 2 m2 g-1, 6 and the surface area for 5-10-µm (80-300 Å) porous particles is between 100 and 300 m2 g-1.37,38 As shown in eq 8, the retention factor, k, also affects the Cs term. The effect of k values on the Cs term was compared for nonporous and porous particles, as shown in Figure 5. At high linear velocity, the k/(k + 1)2 values measured for the two types of particles were very close to each other. Therefore, the higher mass-transfer resistance for nonporous particles is mainly due to (34) Hanson, M.; Kurganov, A.; Unger, K. K.; Davankov, V. A. J. Chromatogr., A 1993, 656, 369-380. (35) Shen, Y.; Lee, M. L. Chromatographia 1995, 41, 665-670. (36) Shen, Y.; Malik, A.; Li, W.; Lee, M. L. J. Chromatogr., A 1993, 656, 369380. (37) Alltech Associates. Chromatography Catalog 400; Deerfield, IL, 1997. (38) Sands, B. W.; Kim, Y. S.; Bass, J. L. J. Chromatogr. 1986, 360, 353-369.

Figure 6. Plots of plate height versus linear velocity for columns packed with 10-µm nonporous and porous particles in SGC. Conditions are the same as in Table 2. Key: b, nonporous particles; O, porous particles (300 Å); 0, porous particles (80 Å).

the thicker film on the particle surface (see Figure 4). It should be noted that the actual mass-transfer process may include an adsorption-desorption mechanism as well as a partition mechanism as shown in eq 8.32,33 The nonequilibrium process of adsorption-desorption in porous particles can result in an extra contribution of mass-transfer resistance to plate height. Considering this factor and the Cstag for porous particles, the net difference of mass-transfer resistance between nonporous and porous particles is not as significant as originally expected. When the mass-transfer resistance term in the stationary phase is included in the van Deemter equation in SGC, the equation becomes more complicated and it is difficult to regress experimental data using this equation. However, a linear relationship between plate height and linear velocity was found at high linear velocity (e.g., >1.5 cm s-1 for 5-µm particles and >3.5 cm s-1 for 10-µm particles). The C values obtained by linear regression are listed in Table 2, and the R2 values for the regression were all greater than 0.98. Table 2 shows that the total mass-transfer terms for nonporous silica (5 and 10 µm) encapsulated with 1-1.5% SE54 were 30-40% higher than those for porous silica (5 µm,120 Å, and 10 µm, 80 Å) encapsulated with 10% SE-54. The results indicate that the advantage of nonporous particles in mobile-phase Analytical Chemistry, Vol. 71, No. 22, November 15, 1999

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Table 3. Relationship between Peak Width at Half Peak Height (w1/2) and Retention Time (t) in SGC

SE-54a

5-µm 10-µm SE-54b 3-µm ODSc

nonporous particles

porous particles

w1/2 ) 0.0331t + ) 0.998 w1/2 ) 0.0261t - 0.0567, R2 ) 0.999 w1/2 ) 0.0193t + 0.1481, R2 ) 1.000

w1/2 ) 0.0206t - 0.0075, R2 ) 0.993 w1/2 ) 0.0245t - 0.1597, R2 ) 0.999 w1/2 ) 0.0224t - 0.1361, R2 ) 0.995

0.0596,d

R2

a Conditions: 30-cm columns, 120 °C, 175 atm for porous particles, 100 atm for nonporous particles. b Conditions: 100-cm columns, 240 atm for porous particles, 140 atm for nonporous particles. c Conditions: 30-cm columns, 80 atm for nonporous ODS, 230 atm for porous ODS (80 Å). Normal hydrocarbons (C8 - C13) were used as test solutes. Other conditions are the same as in Table 2. d w1/2 and t in this table have units of s.

Figure 7. Peak capacities for 5-µm nonporous and porous particles. Conditions: (A) 55 cm, 100 atm, u ) 5.3 cm s-1, nonporous particles; (B) 55 cm, 175 atm, u ) 5.3 cm s-1, porous (120 Å) particles; (C) 55 cm, 100 atm, u ) 2.1 cm s-1, porous (120 Å) particles; other conditions are the same as in Table 3 for 5-µm particles.

Figure 8. Peak capacities for 3-µm nonporous and porous particles. Conditions: (A) 30 cm, 80 atm, u ) 1.9 cm s-1, nonporous ODS; (B) 30 cm, 230 atm, u ) 1.9 cm s-1, porous ODS (80 Å); (C) 5 cm, 140 atm, u ) 2.5 cm s-1, porous ODS (80 Å); other conditions are the same as in Table 3.

mass transfer over porous particles is overcome by the disadvantage in stationary-phase mass transfer in SGC. As shown in Figure 6, the column efficiency obtained from columns packed with polymer-encapsulated porous particles is also affected by particle pore size. The column packed with 80-Å particles produced a lower C term compared to that with 300-Å particles. This may be because 80-Å particles have a higher surface area, and thus a thin film can be formed on the surface. However, both columns provided lower C terms than the column packed with 10-µm nonporous particles. This conclusion is in agreement with that observed from 5-µm particles. In summary, total mass-transfer resistance for typical nonporous particles encapsulated with a polymer is higher than that for polymer-encapsulated porous particles because of the lower surface area and, thus, thicker stationary-phase film on the nonporous particle surface. Therefore, polymer-encapsulated porous particles are more suitable for fast separations than nonporous particles in SGC when the same linear velocity is used. We successfully separated various environmentally important compounds within 1-5 min using a 30-cm column packed with 5-µm polymer-encapsulated porous particles.39 It should be noted that in order to produce the same linear velocity, a column packed with porous particles requires higher inlet column pressure because it has lower column permeability than a column packed

with nonporous particles (see Figure 2). For SGC, a commercial SFC pump can readily meet this requirement because the viscosity of the mobile phase under SGC conditions is much lower than that of liquids and supercritical fluids. Peak Capacity. In the separation of mixtures containing many components, attention should focus on the total number of peaks separable rather than on the resolution of specific pairs.40 In this case, peak capacity is the best index to characterize the separation power of a column. Equation 6 was established on the basis of the experimental observation that there is a linear relationship between peak width at half-height (w1/2) and retention time under isothermal and isobaric conditions. It was successfully used for the calculation of peak capacities for columns and conditions of separations that required long times. In this study, we investigated the suitability of this equation for fast separations using nonporous and porous particles. The linear velocities used for the determination of peak capacity in this study were much higher than optimized linear velocities. Table 3 lists the experimental results under fast SGC conditions; the R2 values for all equations were greater than 0.99. This indicates that the proposed peak capacity eq 6 is also valid for fast SGC. Comparing the relationships in Table 3 with eq 5, values for the constants a and b were found, and peak capacities for the

(39) Wu, N.; Shen, Y.; Lee, M. L. J. High Resolut. Chromatogr. In press.

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(40) Giddings, J. C. Unified Separation Science; John Wiley & Sons: New York, 1991; Chapter 5.

Figure 9. SGC chromatograms for 3-µm nonporous and porous particles. Conditions: (A) 30 cm, 80 atm, nonporous ODS; (B) 30 cm, 230 atm, porous ODS (80 Å); (C) 5 cm, 140 atm, porous ODS (80 Å); other conditions are the same as in Figure 8. Peak identifications: (1) CS2, (2) n-C8, (3) n-C9, (4) n-C10, (5) n-C12, and (6) n-C13.

various columns were calculated using eq 6. Figure 7 shows the calculated peak capacities of 30-cm columns packed with 5-µm nonporous and porous particles encapsulated with SE-54. It can be seen from the figure that, at the same linear velocity of 2.9 cm s-1 (the same t0), the peak capacity for the column packed with porous particles was higher than for the column packed with nonporous particles, where the effect of column efficiency on peak capacity is dominant. However, when the same column inlet pressure was used, the dead time for the porous particle packed column was higher by 2.5 times than that for the nonporous packed column; therefore, the peak capacity for the column packed with porous particles was lower (see eq 7), where the effect of dead time on peak capacity is pronounced. When the time interval reaches more than 90 s, the peak capacity for the column packed with porous particles is higher again than that for the column packed with nonporous particles, where the effect of dead time on peak capacity is less significant. This result implies that the column packed with porous particles is more suitable for separations of complex samples, even though the same column inlet pressure is used. In addition to column efficiency and dead time, the constant b in eq 6 also affects the column peak capacity. Comparing the b values in equations listed in Table 1, it can be seen that the b values for porous particles are all greater than those for nonporous particles. This may be ascribed to the greater retention factors for porous particles, although no quantitative relationship has been found between the b value and the retention factor. The average ratio of retention factors for porous ODS to those for nonporous ODS was found to be ∼13 at the same linear velocity using a 30cm column packed with 3-µm particles. This ratio is much higher than that (∼3.5) for porous and nonporous SE-54 particles. Thus, among the columns in Table 3, the columns packed with ODS

particles exhibited the greatest difference in b values between porous and nonporous particles. The peak capacities for columns packed with bonded nonporous and porous ODS were compared in Figure 8. It can be seen that when the same linear velocity (t0 ) 16 s) was used, the peak capacity for the porous ODS column was higher than for nonporous ODS although the separation time was longer (Figure 9A and B). However, when a short column (5 cm) packed with 3-µm porous ODS was used, high-speed separations were achieved (see Figure 9C). This short column produced a very short dead time (2 s) and, thus, high peak capacity within a short time interval, as illustrated in Figure 8. Therefore, a short column packed with porous particles is more suitable for highspeed separations in SGC. Jonker and Popper separated four gaseous hydrocarbons within 1 s using a 3-cm column packed with porous silica in GC.41 It should be noted that when the time interval increases to more than 45 s (see Figure 8), the peak capacity for the short column is less than that for the longer columns because the column efficiency is a major factor affecting peak capacity. This means that short columns cannot be used for separations of complex samples because they produce low total column efficiency. CONCLUSIONS Due to the low density of the mobile phase in SGC, the Cstag term for porous particles is not significant compared to that in LC and SFC. In SGC, the mass-transfer resistance in the stationary phase and longitudinal diffusion are more important. Total masstransfer resistance for typical nonporous particles encapsulated with 1-1.5% SE-54 is higher than that for porous particles encapsulated with 10% SE-54 because of the lower surface area (41) Jonker, R. J.; Popper, H. Anal. Chem. 1982, 54, 2447-2456.

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and, thus, thicker stationary-phase film on the nonporous particle surface. Polymer-encapsulated porous particles are more suitable for fast separations than nonporous particles when the same linear velocity is used in SGC; however, high inlet column pressure is required. The peak capacities for columns packed with porous particles are higher compared to those for columns packed with nonporous particles. This may be mainly due to the high column efficiency and greater capacity factors of columns containing

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porous particles when retained solutes are used. High-speed separations can be achieved using very short columns packed with small porous particles. Received for review June 15, 1999. Accepted August 22, 1999. AC990650P