Temperature-Jump Investigation of Alkyl Chain Length Effects on

From a fit of the data to a two-step kinetic model, the rates of both adsorption and partition of the ionic probe on the C4 chain are estimated; both ...
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Anal. Chem. 1996, 68, 1651-1657

Temperature-Jump Investigation of Alkyl Chain Length Effects on Sorption/Desorption Kinetics at Reversed-Phase Chromatographic Interfaces F. Y. Ren and J. M. Harris*

Department of Chemistry, University of Utah, Salt Lake City, Utah 84112

The influence of the alkyl chain length on the kinetics of solute retention at reversed-phase chromatographic surfaces is examined. A Joule-discharge temperature-jump relaxation experiment was used to monitor reversible sorption/desorption kinetics at C4- and C8-modified silica/solution interfaces. Biexponential sorption/desorption relaxation kinetics were observed for a charged fluorescent probe, 1-anilino-8-naphthalenesulfonate (ANS), on both C4- and C8-silica surfaces. Both relaxation rates on C4 surfaces were sufficiently slow to be measured and increased linearly with solute concentration. One of the relaxations on a C8 surface is too fast to be resolved from the heating rate, similar to behavior of the solute on a longer chain C18-silica. These observations suggest that sorption kinetics on the intermediate chain length surfaace, C4-silica, are different from kinetics on longer chain length surfaces, C8- and C18-silica. From a fit of the data to a two-step kinetic model, the rates of both adsorption and partition of the ionic probe on the C4 chain are estimated; both rates exhibit significant influence over the equilibrium constant. The relaxation rate of a neutral probe, N-phenyl-1-naphthylamine, is also measured; the results indicate a fast (diffusion-controlled) adsorption step, followed by a detectable barrier to partition that is similar to the partition barrier for ANS on the C4-silica surface. These results show that the alkyl chain length of modified silica strongly influences retention kinetics. Reversed-phase liquid chromatography has become widely used as a method for chemical separation. Despite its widespread application, understanding the chemistry of solute retention in reversed-phase chromatography remains a challenge due to the complexity of solvation and interfacial phenomena that govern retention and the difficulty of collecting relevant structural and kinetic data at a liquid/solid interface. Several mechanistic factors have been identified to describe solute retention in reversed-phase chromatography, including retention dominated by partition of solutes in the bonded alkyl chains,1,2 adsorption of solutes at the solution/alkyl chain interface3,4 mixed adsorption and partition models,5 and solute interactions in the solution phase.6 Experi(1) Dill, K. A. J. Phys. Chem. 1987, 91, 1980-1988. (2) Marqusee, J. A.; Dill, K. A. J. Chem. Phys. 1986, 85, 434-444. (3) Colin, H.; Guiochon, G. J. Chromatogr. 1977, 141, 289-312. (4) Unger, K. K.; Becker, N.; Roumeliotis, P. J. Chromatogr. 1976, 125, 115127. (5) Rehak, V.; Smoolkova, E. Chromatographia 1976, 9, 219-229. (6) Karger, B. L.; Gant, J. R.; Hartkopf, A.; Weiner, P. H. J. Chromatogr. 1976, 128, 65-78. 0003-2700/96/0368-1651$12.00/0

© 1996 American Chemical Society

mentally, retention mechanisms have generally been studied by measuring chromatographic elution profiles of various solutes. System parameters such as mobile-phase composition, bondedphase chain length and density, and temperature are varied to determine their influences on solute retention.7-10 Since conventional chromatographic studies often fail to provide sufficient information to distinguish between various models, additional data about the structure of the stationary phase and the environment of solute probes have been acquired using NMR, ESR, IR, and fluorescence spectroscopies.11-15 More recently, the kinetics of solute sorption/desorption at reversed-phase interfaces have been investigated by relaxation methods using temperature- and pressure-jump perturbations.16-22 Nearly every mechanism proposed for solute retention indicates that it is related to the surface concentrations of bonded ligands and their chain lengths. Early studies discussed the linear relationships between capacity factor values (k′) and surface coverage and alkyl chain length of the stationary phase, which impact the phase ratio, under the assumption that the retention is determined by the area of contact between the hydrophobic moiety of the solute and the stationary phase.23 In general, increased carbon content or chain length results in greater retention under given mobile-phase conditions.24 Contrary to early investigations, Berendsen and Galan25 did not observe a continuous increase in retention with increasing (7) Dorsey, J. G.; Cooper, W. T. Anal. Chem. 1994, 66, 857A-867A. (8) Melander, W.; Stoveken, J.; Horvath, C. J. Chromatogr. 1980, 199, 35-56. (9) Sentell, K. B.; Dorsey, J. G. J. Chromatogr. 1989, 461, 193-207. (10) Schoenmakers, P. J.; Billiet, H. A. H.; Galan, L. D. Chromatographia 1982, 15, 205-214. (11) Sindorf, D. C.; Maciel, G. E. J. Am. Chem. Soc. 1983, 105, 1848-1851. (12) Gilpin, R. K. J. Chromatogr. Sci. 1984, 22, 371-377. (13) Wright, P. B.; Lamb, E.; Dorsey, J. G.; Kooser, R. G. Anal. Chem. 1992, 64, 785-798. (14) Sander, L. C.; Callis, J. B.; Field, L. R. Anal. Chem. 1983, 55, 1068-1075. (15) Lochmuller, C. H.; Colborn, A. S.; Hunnicutt, M. L.; Harris, J. M. J. Am. Chem. Soc. 1984, 106, 4077-4082. (16) Marshall, D. B.; Burns, J. W.; Conolly, D. E. J. Chromatogr. 1986, 360, 13-24. (17) Marshall, D. B.; Burns, J. W.; Conolly, D. E. J. Am. Chem. Soc. 1986, 108, 1087-1088. (18) Waite, S. W.; Harris, J. M.; Ellison, E. H.; Marshall, D. B. Anal. Chem. 1991, 63, 2365-2370. (19) Ellison, D. B.; Waite, S. W.; Marshall, D. B.; Harris, J. M. Anal. Chem. 1993, 65, 3622-3630. (20) Waite S. W.; Marshall, D. B.; Harris, J. M. Anal. Chem. 1994, 66, 20522061. (21) Waite, S. W.; Holzwarth, J. F.; Harris, J. M. Anal. Chem. 1995, 67, 13901399. (22) Ren, F. Y.; Waite, S. W.; Harris, J. M. Anal. Chem. 1995, 67, 3441-3447. (23) Horvath, C.; Melander, W.; Molnar, I. J. Chromatogr. 1976, 125, 129-156. (24) Roumeliotis, P.; Unger, K. K. J. Chromatogr. 1978, 149, 211-224. (25) Berendsen, G. E.; Galan, L. D. J. Chromatogr. 1980, 196, 21-37.

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chemically bonded alkyl chain length. Instead, the retention increases rapidly from the shortest chain length (C1) up to a certain chain length, after which the retention gradually levels off. The “critical chain length” where the retention begins to become constant lies between 8 and 10 carbon atoms in the alkyl bonded chain. Two studies26,27 have shown a similar improvement in retention selectivity with increasing chain length up to ∼C12 after which it reaches a constant value that could be predicted from n-alkane/mobile phase liquid/liquid extraction equilibria.27 These chromatographic data indicate that the retention of solutes on shorter alkyl chains is sensitive to the finite size of surface ligands and their bonding to the silica substrate. To exploit the full potential of reversed-phase chromatography for efficient separation of complex mixtures as well as for detailed understanding of solute retention, a knowledge of kinetic phenomena underlying the retention process is required. Mechanisms of solute sorption/desorption kinetics at short-chain (C1)21,22 and long-chain (C18) stationary phases20 have been previously investigated. A finite rate of adsorption of an ionic solute was measured on both C1- and C18-silica surfaces; a comparable neutral probe adsorbed to both surfaces at a diffusion-controlled rate with no detectable barrier.20-22 For the C18-silica surface, a second sorption event was detected and assigned to partitioning of the solute into the C18 chains; the rate was too fast to measure. To establish how chain length affects retention kinetics and the mechanism of reversed-phase sorption, it is necessary to study these kinetics on intermediate chain length surfaces. In the present work, the influence of the alkyl chain length on sorption/ desorption kinetics at reversed-phase chromatographic interfaces is examined. We employ a Joule-heating temperature-jump perturbation to study the relaxation kinetics of sorption of simple ionic and nonionic fluorescent solutes at C4- and C8-silica/solution interfaces. EXPERIMENTAL SECTION Materials. The porous silica gel used as a substrate in this study, Licrosorb Si-60 (5 µm particle size), had a mean pore diameter of 60 Å and a surface area of 550 m2/g (by N2 BET). Butyldimethylchlorosilane (C4), n-octyldimethylchlorosilane (C8), and trimethylchlorosilane (TMCS) were purchased from Petrarch. The C4- and C8-modified silica were prepared in-house and also were end-capped with TMCS to reduce the number of free silanol groups. Elemental carbon and hydrogen analysis was performed by M-H-W Laboratories (Phoenix, AZ). The bonded silicas were found to have a specific fraction of 7.43% carbon and 1.69% hydrogen for C4-modified silica and 20.18% carbon and 4.22% hydrogen for C8-modified silica; end-capping with TMCS made only a small (0.2%) contribution to the carbon content of the modified silicas. The ligand coverage is estimated from the elemental analysis results and the N2 BET surface area to be 1.87 µmol/m2 for C4 and 3.08 µmol/m2 for C8. Solvents used were methanol, toluene, chloroform, tetrahydrofuran, and acetonitrile, all spectral grade (OmniSolve), and water was doubly distilled and deionized. The columns used for chromatographic measurements were 4.6 mm i.d. × 50 mm and were slurry packed according to a procedure described previously.20 The ionic probe 1-anilino-8-naphthalene sulfonate ammonium salt (ANS) (Aldrich), and the nonionic probe, N-phenyl-1-naph(26) Majors, R. E.; Hopper, H. J. J. Chromatogr. Sci. 1974, 12, 767-778. (27) Lochmuller, C. H.; Wilder, D. R. J. Chromatogr. Sci. 1979, 17, 574-579.

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thylamine (1-NPN) (Aldrich), were used as received. Sodium chloride (Mallinckrodt) was added as electrolyte in both temperature-jump experiments and chromatographic measurements. ANS and 1-NPN show a much stronger fluorescence intensity in hydrophobic (nonpolar) environments than in to hydrophilic (polar) environments. Chromatography. Chromatographic data were obtained with a high-performance liquid chromatography (HPLC) system consisting of a Beckman Model 210 injector, an Isco Model 2350 isocratic pump, a 50 mm × 4.6 mm i.d. Licrosorb 5 µm Si-60 C4 column packed in-house, and a Isco Model 229 UV/visible absorbance detector operated at 253 nm. An Eppendorf CH-30 column heater coupled with an Eppendorf TC-50 temperature controller was added to the system for measuring the sorption enthalpy. Sorption isotherms were measured by the frontal elution method28 using a dual-pump20 system with detection by a Beckman model 153 UV/visible detector operated at 365 nm. Spectral grade methanol (OmniSolve) was used without further purification. The mobile phase used for these studies was methanol/water ranging from 70/30 to 30/70 (v/v). Mobile-phase components were sparged with helium 10 min. All methanol/ water mobile phase was premixed (v/v) in the appropriate proportions and degassed by sonicating for 15 min prior to use. Mobile-phase flow rate for all experiments was 1.0 mL/min. Retention of the ANS molecules was determined relative to D2O as a dead-volume marker. Sorption/Desorption Kinetic Measurements. The Jouleheating temperature-jump system previously described18,20,22 was designed to contain a packed bed of alkylated silica and to simulate chromatographic conditions. The loading of the silica samples into the cell was accomplished by slurry injection. Aqueous methanol solutions containing sodium chloride and probe molecules were then pumped through the sample cell at 0.1 mL/min by a Beckman Model 110A HPLC pump. The experimental measurements were carried out every 90 s and averaged until a reasonable signal-to-noise ratio was achieved. Temperature-jump relaxation kinetic signals were acquired for ANS in 50/50 (v/v) and for 1-NPN in 70/30 (v/v) methanol/water mobile phase with 0.4 M NaCl. In all cases, the fluorescence intensity decreased on a time scale of microseconds and showed the same tendencies for ANS and 1-NPN on C1- and C18-silica. A decrease in fluorescence intensity is consistent with the negative enthalpy of sorption. RESULTS AND DISCUSSION Sorption of Probes on Intermediate Chain Length Alkylated Silica. Chromatographic measurements were carried out to test the feasibility of the temperature-jump kinetic experiments on intermediate chain length silicas and to determine the conditions for optimum relaxation signals. Van’t Hoff plots were prepared for both ANS and 1-NPN probes on C4- and C8-silica in a series of mobile phase solvent compositions (methanol/water 40/60, 50/50, and 60/40 (v/v)), and the results are summarized in Tables 1 and 2. In all cases, ln k′ was linear with 1/T over the modest 30° range (r2 g 0.98), and the enthalpies of adsorption were large, more than sufficient for temperature-jump experiments. The smallest enthalpy change observed, ∆H ) -11.9 kJ/ mol, corresponds to the relative change of the equilibrium constant (28) Katti, A. M.; Gruochon, G. A. In Advances in Chromatography, Vol. 31; Giddings, J. C., Ed.; Marcel Dekker: New York, 1991; Chapter 1.

Table 1. Sorption Enthalpies of 1-Anilino-8-naphthalenesulfonate versus Solvent Compositiona MeOH/H2O (v/v)

r2 b

∆H (kJ/mol)

MeOH/H2Oa

k′(C1)b

k′(C4)

k′(C8)

k′(C18)c

30/70 40/60 50/50

0.994 0.992 0.982

-20.7 ( 1.2 -16.5 ( 1.1 -11.9 ( 1.2

50/50 60/40 70/30 80/20

8.10 2.95 1.08

20.58 7.50 2.56

10.51

44.5 11.1 4.2

a The stationary phase is C4-silica with methanol/water and 0.4 M NaCl mobile phase; [ANS] ) 25 µM. b Correlation coefficient for a linear fit of the van’t Hoff plot.

Table 2. Adsorption Enthalpies of N-Phenyl-1-naphthylamine versus Solvent Compositiona MeOH/H2O (v/v)

r2

∆H (kJ/mol)

60/40 70/30

0.993 0.994

-18.4 ( 1.1 -12.1 ( 0.6

a The stationary phase is C4-silica with methanol/water mobile phase; [1-NPN] ) 25 µM.

Table 3. Chromatographic Retention of ANS versus Solvent Composition on C1-, C4-, and C18-Silica Columns MeOH/H2Oa

k′(C1)b

k′(C4)

k′(C8)

k′(C18)c

40/60 50/50 60/40 70/30 80/20

6.82 2.47 0.95 0.28

16.5 4.54 1.32 0.66

13.8 3.28 1.41

15.2 3.40 1.80 0.94

a

Table 4. Chromatographic Retention of 1-NPN versus Solvent Composition on C1-, C4-, and C18-Silica Columns

Includes 0.4 M NaCl. b Data from ref 22. c Data from ref 20.

with temperature, ∆K/K ) -1.6% per degree of temperature rise at 298 K. Since Joule-heating can raise the temperature of a packed bed of 5 µm porous silica by more than 10° in a few microseconds,18,19 the sorption enthalpies are sufficient large to generate a significant perturbation to the sorption equilibrium (∆K/K g -16%). It was found from Table 1 that ∆H values became more negative as the water content of the mobile phase was increased, indicating that it became energetically more favorable for the solute to be in the stationary phase. Similar trends are also observed for the nonionic fluorescent probe (1NPN) on C4-silica gel surface (Table 2). This phenomenon is consistent with the retention being primarily driven by the enthalpy change and not being a hydrophobic interaction.7,29 To poise the equilibrium for relaxation measurements, retention measurements for ANS and 1-NPN were made for a series of solvent compositions on C4- and C8-silica. The results are summarized in Tables 3 and 4, along with data from the literature comparing retention on C1- and C18-silica (see below). As expected, the capacity factors increase with increasing fraction of water in the mobile phase. In perturbation experiments, the largest relaxation amplitude occurs when the fraction of molecules in the product and reactant forms at equilibrium is 0.5.30 At this condition, the relative change in the number of moles of product is most sensitive to a change in the equilibrium constant; the (29) Cole, L. A.; Dorsey, J. G. Anal. Chem. 1992, 64, 1317-1323. (30) Bernasconi, C. F. Relaxation Kinetics; Academic Press: New York, 1976.

a

Includes 0.4 M NaCl. b Data from ref 22. c Data from ref 20.

relative amplitude becomes smaller on either side of this value. For a sorption equilibrium, the fraction of solute on the surface is given by k′/(1 + k′), which should equal 0.5 for a maximum relaxation amplitude, which corresponds to a value of k′ ) 1.0. In Table 3, the largest relaxation amplitudes for ANS on C4-silica, for example, are anticipated to occur for 60/40 methanol/water solutions. In the kinetic results presented below, however, we observe the strongest relaxation signals with a 50/50 methanol/ water solution phase. One reason for lower sensitivity with higher methanol concentrations is that these solutions correspond to a smaller enthalpy of sorption, resulting in a smaller perturbation to the equilibrium according to the Van’t Hoff equation. Another reason for the smaller relaxation amplitude is that the fluorescence quantum yield of ANS in the mobile phase increases with methanol concentration in solution, producing a smaller difference in the fluorescence signal upon sorption to the C4-silica surface. Since the relaxation kinetics were not single-exponential for ANS on C4-silica (see below), a sorption isotherm was measured for ANS to determine whether the retention mechanism for this solute was homogeneous on the intermediate chain length surface. The isotherm was measured by frontal elution chromatography, whereby a series of ANS solutions of increasing solute concentration is pumped through the column. After the solute comes to equilibrium with the alkylated surface, excess solute elutes from the column, and a “breakthrough” curve is measured to determine the amount of solute sorbed on the column packing.28 The isotherm was measured over 6 ANS concentrations ranging from 10 to 500 µM in 50/50 methanol/water (v/v) with 0.4 M NaCl, yielding surface concentrations ranging from 0.21 to 11.10 nmol/ m2; these are nearly 3 orders of magnitude below a full monolayer of sorbed probe. The isotherm in this region is a straight line (r2 ) 0.999 998), indicating that a single sorption mechanism is responsible for ANS retention over the concentration range investigated. From the chromatographic retention measurements, a strong influence of alkyl chain length on retention can be observed. Tables 3 and 4 compare the capacity factors for retention with several solvent compositions for ANS and 1-NPN on C1-, C4-, C8-, and C18-bonded alkyl chain stationary phases. While the tabulated capacity factors show a marked increase in retention for increasing chain length from C1 to C8, with little change from C8 to C18, a quantitative comparison should be made at the same column packing density and ligand surface coverage, since these factors proportionally influence the measured capacity factor by changing the phase ratio. Since these two factors are experimentally difficult to control, a corrected capacity factor, ko′, was calculated by normalizing the measured k′ values to the packing and ligand densities of the C1 column: ko′ ) kCn′FC1 θC1/FCnθCn, where FCnθCn are the packing and ligand densities for the CnAnalytical Chemistry, Vol. 68, No. 9, May 1, 1996

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Figure 1. Capacity factors versus alkyl chain length. Measured k′ is corrected for packing and ligand density (see text). Squares are ANS eluted with 50/50 methanol/water; triangles are 1-NPN eluted with 70/30 methanol/water; mobile phases also contain 0.4 M NaCl.

silica. The logarithms of the capacity factors, corrected for small differences in packing and ligand density, are plotted in Figure 1 for ANS eluted with 50/50 methanol/water and for 1-NPN eluted with 70/30 methanol/water mobile phase. The retention of both compounds shows a strong dependence on the length of the alkyl chain up to C8 and a much weaker dependence from C8 to C18; extrapolating the trend of the first three points of both sets of data to ko′ for C18 indicates a “critical chain length” of 10-12 carbons, consistent with previous results reported in the literature.25-27 These data support the idea that both probe molecules partition into the bonded phase to a degree which begins to saturate for C8 ligands, which is also consistent with the relaxation kinetic results discussed below. Temperature-Jump Relaxation Results. Temperature-jump relaxation kinetics were obtained for ANS sorption to C4-silica surfaces from 50/50 (v/v) methanol/water mobile-phase solvent containing 0.4 M NaCl electrolyte to carry the discharge current. As in previous studies of C1 and C18 surfaces,22,20 the fluorescence intensity from the probe decreased with increasing temperature of the sample, which is consistent with the negative enthalpy of sorption and the lower fluorescence yield of the probe molecule in the polar solution phase. An example relaxation transient is shown in Figure 2. The kinetic form of the relaxation on C4silica is not only different from the slow, single-exponential decay measured for adsorption to a C1-silica,22 but also different from sorption to a longer chain, C18-silica, which produced one slow relaxation and a second too fast to resolve from the heating rate.20 The relaxation data for this intermediate chain length fit a biexponential model, with both relaxation rates being slow and of comparable magnitude. Figure 2 shows the quality of fit to this biexponential model, which includes convolution with the known rate of decay of Joule-discharge heating; the residuals errors between the model and the experimental data are random. Both relaxation rates varied with concentration of the solute in solution, so they are carrying information about the rate of sorption of the solute from the mobile phase (see below). The relaxation rate of a neutral probe, 1-NPN, was also measurable on the C4-silica surface, which indicates that a barrier to sorption is detectable on this surface, whereas no barrier could be detected for this probe on C1 or C18 surfaces.22,20 Figure 3 shows a relaxation trace for 10 µM 1-NPN in 70/30 (v/v) methanol/water with 0.4 M NaCl on the C4-silica surface, with a fit to a single-exponential relaxation (convoluted with the rate of heating). Tables 5 and 6 list the relaxation data on C4-silica for ANS and 1-NPN in 50/50 and 70/30 (v/v) methanol/water mobile 1654 Analytical Chemistry, Vol. 68, No. 9, May 1, 1996

Figure 2. Temperature-jump relaxation for ANS sorption on C4modified silica. A representative relaxation trace and corresponding biexponential fit and residual error for 50/50 methanol/water with 0.4 M NaCl and 10 µM ANS in the solution phase. A least-squares fit to biexponential decay with rates 1/τ1 ) (17.3 ( 6) × 104 s-1, 1/τ2 ) (25.0 ( 11) × 104 s-1.

Figure 3. Temperature-jump relaxation for 1-NPN sorption on C4silica. Solution conditions are 70/30 MeOH/H2O with 0.4 M NaCl; [1-NPN] ) 1.0 × 10-4 M. A least-squares fit to a single-exponential relaxation with rate 1/τ ) (15.9 ( 0.9) × 104 s-1.

phases, respectively. As a further check of the chain length dependence of sorption/desorption kinetics, the relaxation of ANS at a C8-silica/solution interface was also tested by the temperaturejump method. The results in Figure 4 show that the kinetic form of the relaxation is identical to that of the longer chain C18-silica,20 where two well-separated relaxation processes are observed. The fast relaxation has a rate that is indistinguishable from the heating rate of the voltage discharge (from a kinetic process that is faster than our instrument response); the slow rate detected is sensitive to the ANS concentration. The relaxation rate for the nonionic 1-NPN probe was checked on C8-silica and determined to be faster

Table 5. Relaxation Kinetics Data for ANS on C4-Silicaa [ANS] × 104 (M)

τ1-1 × 10-4 (s-1)

τ2-1 × 10-4 (s-1)

0.10 1.25 2.50 5.00

17.3 ( 6.5 20.6 ( 1.8 28.7 ( 7.5 30.5 ( 5.1

25 ( 11 58 ( 24 60 ( 20 80 ( 12

a

stationary phase

MeOH/H2O (v/v)

kads × 10-8 (M-1 s-1)

kdes × 10-4 (s-1)

C1

60/40 50/50 50/50 60/40

5.9 ( 0.1 10.5 ( 1 12.7 ( 3 4.9 ( 0.9

1.14 ( 0.09 0.55 ( 0.1 107 ( 15

C4 C18

Solvent composition is 50/50 methanol/water with 0.4 M NaCl.

Table 6. Relaxation Kinetics Data for 1-NPN on C4-Silicaa

a

Table 7. Alkyl Chain Length Dependence of Adsorption/Desorption Kinetics for ANS

[NPN] × 104 (M)

k(obs) × 10-4 (s-1)

0.50 0.75 1.0

14.0 ( 1.4 14.6 ( 0.8 15.9 ( 0.9

Solvent composition is 70/30 methanol/water with 0.4 M NaCl.

Figure 4. Temperature-jump relaxation for ANS adsorption on C8silica. Solution conditions are 50/50 MeOH/H2O with 0.4 M NaCl; [ANS] ) 50 µM. A least-square fit to a biexponential model with a fast step equal to the heating rate (1/τ ) 5 × 105 s-1) and a slow rate where 1/τ ) (6.9 ( 0.2) × 104 s-1.

than the voltage discharge, with no detectable slow relaxation; again, the kinetic behavior is identical with that of the C18-silica. Interpretation of Sorption/Desorption Kinetic Results. Biexponential sorption/desorption relaxation kinetics on C4-silica could arise from inhomogeneous sorption sites and a mixed retention mechanism. The sorption isotherm results (see above) were, however, linear over the range of ANS concentrations used in the kinetic experiments, indicating that the sorption equilibrium is homogeneous. Note that the retention homogeneity of ANS here is due in part to the high-ionic-strength mobile-phase conditions; isotherms and elution peak shapes for this solute in the absence of added electrolyte are inhomogeneous on C1-silica surfaces,21 probably due to interactions with surface charges from deprotonated silanols on the silica substrate. Addition of electrolyte compresses the electrical double layer at the silica surface and reduces interactions between the charged solute and the surface, producing homogeneous sorption interactions.21 Another possible explanation for the observation of of two relaxation rates for ANS on a C4-silica surface could be sorption kinetics at sites of the same energy but different kinetic accessibility. Collision rates of molecules with the surface of porous

silica have been shown to be sensitive to the pore geometry,31 and temperature-jump experiments have been shown to probe kinetics with the interior pore structure of the silica.18 A population of accessible sorption sites could give rise to a faster relaxation rate, while a slow response could be due to surface sites in more restricted pores. In a study of pore connectivity in alkylated silicas,19 it was established that shorter alkyl ligands result in fewer pore closures and more efficient transport kinetics within the material. If pore geometry were a source of dispersion in surface site accessibility, then sorption/desorption kinetics in C1-derivatized silica would have a larger fraction of accessible (fast) sites compared to C4-silica. ANS relaxation kinetics on a C1 phase prepared on the same silica substrate22 showed no evidence of dispersion in site accessibility; the kinetics on this material were homogeneous (single-exponential) and slow. Therefore, the inhomogeneous kinetics on the C4 material do not arise from a dispersion in transport rates to the silica surface. Based on the similarity of the relaxation rate for ANS adsorption to C1-silica to the slow component of biexponential relaxation on C18-silica, a two-step adsorption-partition model has been proposed,20 The slower rate was assigned to adsorption of solute from solution, since the rate was proportional to solution concentration for both C1 and C18 surfaces;22,20 from the slopes of the relaxation rate versus ANS concentration, the adsorption rate constants were indistinguishable for the two surfaces (see Table 7). The additional, fast relaxation rate on C18 was assigned to the adsorbed probe partitioning into the C18 layer.20 Since ANS adsorption onto C1-silica and sorption into C4, C8, and C18 ligands appear to all share a common slow adsorption step (see Table 7 and analysis below), it is anticipated that biexponential relaxation kinetics of ANS sorption at C4, C8, and C18 surfaces all arise from the same two-step adsorption/partition process. The second, fast partitioning step, which is too fast to follow with our experiment on C8 and C18 surfaces, appears to slow down on a C4-silica and become comparable in rate to the adsorption step. This is a reasonable result, since the partitioning rate should be related to bonded chain mobility, which is reduced for shorter alkyl chains. From both NMR32 and ESR33 studies, it has been found that the bonded phase mobility increases from the point of chain attachment at the surface to the terminal alkyl group, resulting from increased motional freedom within the chain with increasing distance from the silica surface. As chain length increased to a certain point, the influence of the chain mobility on the kinetic barrier to partitioning could be negligible. This leads to the postulate that the kinetic barrier of partitioning on alkylated (31) Wong, A. L.; Hunnicutt, M. L.; Harris, J. M. J. Phys. Chem. 1991, 95, 44894495. (32) Albert, K.; Pfleiderer, B.; Bayer, E. Chemically Modified Oxide Surfaces. In Chemically Modified Surfaces, Vol. 3; Leyden, D. E., Collins, W. T., Eds.; Gordon & Breach: New York, 1990; pp 233-243. (33) Ren, F. Y.; Rapoport, N.; Harris, J. M. Manuscript in preparation.

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reversed-phases depends on chain length, where the barrier decreases with increasing chain length up to a critical chain length. Thus, the kinetic response for C8 and C18 would be indistinguishable, with an initial slow adsorption step, followed by rapid partitioning into the chains. To quantitatively analyze the kinetic response for sorption into the intermediate, C4-silica surface phase, a kinetic model for adsorption/partition needs to be developed in which both rates are measurable. The mechanism for this process is given by kads

kp

Msoln + S \ yk z Mads y\ z Mpart k des

(1)

-p

where kads is the bimolecular rate constant for adsorption of the solute to the surface, S, and kdes is a unimolecular rate constant for desorption of the solute from the surface, kp is a rate constant for partitioning of the solute into the alkyl phase, and k-p is a rate constant for departitioning of the solute. The adsorption processes for the ionic probe, ANS, at C1, C4, C8, and C18 for the first step in eq 1 should be identical; the rate of relaxation for this step should vary linearly with the concentration of the solute in solution with a common rate constant. The partitioning process (second step in eq 1) should depend on alkyl chain length. At C1-silica, however, only an adsorption step was observed, since the methyl ligands do not allow solute intercalation or partitioning into a surface phase; this leads to the observed single-exponential relaxation on C1-silica. At C8- and C18-silicas, the partitioning rate constant is much faster than the adsorption rate, so the adsorption process is rate-limiting. For a kinetic mechanism having sequential slow and very fast first-order steps, the relaxations can be separated.30,20 The rate of the fast relaxation is given by

(2)

1/τ1 ) kp + k-p

Figure 5. Sum of relaxation rates on C4-silica, (τ1-1 + τ2-1) versus ANS concentration. Weighted linear least-squares fit to eq 4 is also shown. Solution conditions are 50/50 MeOH/H2O with 0.4 M NaCl.

By plotting the sum of the observed relaxation rates (τ1-1 + τ2-1) versus ([Msoln] + [S]) (plot 1) and their product (τ1-1τ2-1) versus ([Msoln] + [S]) (plot 2), the four rate constants are determined as follows: kads ) slope(1); kdes ) intercept(1) - slope(2)/slope(1); k-p ) intercept(2)/kdes; and kp ) intercept(1) - kdes - k-p. In principle, this approach appears straightforward. However, the concentration of surface sites, [S], as they affect a collision rate with the surface, is not well defined for porous silica due to the inhomogeneous geometry of the pore network. Therefore, only the adsorption rate, kads, and kads[kp + k-p] can be determined unambiguously from the slopes of (τ1-1 + τ2-1) and (τ1-1τ2-1) versus [Msoln]. Nevertheless, desorption, partition, and departition rates can be estimated without knowledge of [S] from the slopes and intercepts of these plots combined with the equilibrium results for these systems. At equilibrium, the ratio of sorbed solute to solute in solution is given by the capacity factor: for the intermediate chain, C4-silica, kC4′ ) (Mads + Mpart)/Msoln; for the methylated C1-silica, kC1′ ) Mads/Msoln, and therefore

which, for C8- and C18-silicas, is too fast to measure, so the observed relaxation follows the heating rate of the experiment. The rate of the observed slow relaxation under these conditions is given by

1/τ2 ) kads([Msoln] + [S]) +

kdesk-p kp + k-p

(3)

Mpart kp kC4′ Mpart + Mads ) )1+ )1+ kC1′ Mads Mads k-p

Thus, partition and departition rate constants can be calculated from

kp + k-p ) Thus, a plot of the slow relaxation rate versus solute, ANS, concentration yielded a slope equal to the adsorption rate constant, kads, and an intercept equal to kads[S] + kdesk-p/(kp + k-p).20 It was observed in the data above that the relaxation kinetics on C4-silica behave differently, with two comparable relaxation rates. The two steps in eq 1 equilibrate at similar rates, so there is strong coupling between the kinetics of the two steps. As a consequence, the observed relaxation times depend on all four rate processes of the system. The equations that describe the observed relaxations for a mechanism having two comparable sequential first-order steps have been derived and solved.30 The relaxation rates are given by

(1/τ1 + 1/τ2) ) kads([Msoln] + [S]) + kdes + kp + k-p

(4)

(1/τ1)(1/τ2) ) kads[kp + k-p]([Msoln] + [S]) + kdesk-p

(5)

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Analytical Chemistry, Vol. 68, No. 9, May 1, 1996

(6)

slope(2) slope(1)

(7)

and

kp/k-p ) 1 - (kC4′/kC1′)

(8)

The capacity factor ratio (corrected for the small differences in column packing and ligand density as above), kC4′/kC1′) 2.47; consequently, kp/k-p ) 1.47 according to eq 8. To determine the adsorption rate, the concentration of ANS is varied in 50/50 (v/v) methanol/water with 0.4 M NaCl mobile phase. It was noted that both relaxation rates on C4-silica depend on the concentration of ANS. Plots of the sum and product of relaxation rates, (τ1-1 + τ2-1) and (τ1-1τ2-1), versus [ANS] are shown in Figure 5 and Figure 6. As predicted by eqs 4 and 5, both the sum and the product of the relaxation rates increase

Figure 6. Product of relaxation rates on C4-silica, (τ1-1τ2-1) versus ANS concentration. Weighted linear least-squares fit to eq 5 is also shown. Solution conditions are 50/50 MeOH/H2O with 0.4 M NaCl.

linearly with [ANS] in the mobile phase, where the slope of the first plot (Figure 5) is equal to the adsorption rate constant, kads ) (12.7 ( 3) x 108 M-1 s-1. The value of kads indicates an adsorption rate that is much slower than a diffusion-controlled limit. Factoring out the adsorption rate constant from the slope of the rate products in Figure 6 gives the sum of partition and departition rate constants: [kp + k-p] ) (0.31 ( 0.05) × 106 s-1. When combined with the ratio of partition and departition rate constants from the capacity factor results (and eq 8) above, these individual rate constants can be determined: kp ) 1.8 × 105 s-1 and k-p ) 1.3 × 105 s-1, respectively. Desorption rates can also be determined directly from the intercepts in Figures 5 and 6. From eq 4, the intercept of the plot of (τ1-1 + τ2-1) versus [ANS] is defined to be intercept(1) ) (kads[S] + kdes+ kp + k-p); from eq 5, the intercept of a plot of (τ1-1τ2-1) versus [ANS] is equal to intercept(2) ) (kads[kp + k-p][S] + kdesk-p). Combining the intercept results with the other parameters determined above to circumvent the lack of information on [S], the desorption rate is estimated according to

(

kdes ) 1 +

)

k-p intercept(1) + kp

(

)

intercept(2) 1 slope(2) kp kp slope(1)

2

(9)

where kdes ) (1.07 ( 0.15) × 106 s-1. The comparison of the chain length dependence of adsorption/ desorption kinetics data is shown in Table 7. The most significant result in this table is that the adsorption rates of ANS onto different chain length alkylated silicas are indistinguishable for the same solution-phase conditions. This agreement strongly supports the two-step adsorption/partition mechanism proposed in eq 3 to interpret the results. It is interesting that the desorption rate of ANS from the C4-silica surface is much faster than that from a C1-silica surface, perhaps due to the greater motion of the alkyl chain compared to that of surface methyl groups. This large

difference in the behavior of adsorption versus desorption rates also indicates a difference in the organization of interfacial solvation upon adsorption, perhaps due to intercalation of methanol into the C4 chains upon adsorption of the ionic probe. The generality of partition/departition kinetics influencing sorption equilibria in intermediate chain reversed-phase chromatography was further tested by using an uncharged probe solute, N-phenyl-1-naphthylamine (1-NPN). Previous kinetic results with this probe had shown no barrier to adsorption from solution onto a C122 or C18 surface.20 Like ANS on C18-20 and C8-silicas (above), the rate of partitioning/departitioning of this probe also could not be detected on a C18 surface.20 On a C4-silica surface, however, the relaxation of this neutral probe to a temperature perturbation occurs at a measurable rate with a single-exponential response. Figure 4 shows the relaxation trace on C4-silica in 70/30 (v/v) methanol/water with 0.4 M NaCl mobile phase, [1-NPN] ) 100 µM. Table 6 lists the relaxation rate versus 1-NPN concentration, which shows that the rate is independent of solute concentration. This is consistent with the studies of 1-NPN on C1-silica which showed that adsorption from solution to a hydrophobic interface of this neutral probe was too fast to be resolved by the Jouleheating experiment. Therefore, the slow rate should reflect the first-order rate of the second, partition step which is not dependent upon concentration from solution; this implies a sequential twostep mechanism where a fast adsorption event is followed by a slow partition step. Since the observed relaxation rate for the partition/departition equilibrium is the sum of kp and k-p (see eq 2), the individual rates can be estimated from the observed rate and the capacity factor ratio for 1-NPN on C4 versus C1-silica (eq 8), kp ) 1.0 × 105 s-1 and k-p ) 0.47 × 105 s-1. These rate constants are similar in magnitude (within a factor 2) to the values of kp and k-p determined above for ANS partition/departition in C4-silica ligands, indicating a similar barrier to penetration of the alkyl chains. For the C4-silica surface, the kinetic barrier to sorption cannot be neglected, even for a neutral solute, due to the slower rate of partition arising from the smaller chain mobility, as discussed above. Relaxation kinetics were also measured for this probe on a C8-silica surface; no detectable barrier to sorption was detected, which was the same diffusion-limited sorption behavior observed with C18 surfaces. The fact that a significant kinetic barrier appears on a short chain length alkylated silica indicates that the sorption kinetics on reversed-phase materials depend on the chain dynamics; based on the 1-NPN results, these effects are found to be independent of slow adsorption from solution that can influence the sorption kinetics of ionic solutes.20-22 ACKNOWLEDGMENT This research was supported in part by the U.S. Department of Energy. Received for review September 18, 1995. February 19, 1996.X

Accepted

AC950935B X

Abstract published in Advance ACS Abstracts, April 1, 1996.

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