Lateral Diffusion of Molecules Partitioned into Silica-Bound Alkyl

Sep 1, 1996 - ... are consistent with a domain model for long-range transport of partitioned molecules through the bound ligands. Fluorescence recover...
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Anal. Chem. 1996, 68, 2879-2884

Lateral Diffusion of Molecules Partitioned into Silica-Bound Alkyl Chains: Influence of Chain Length and Bonding Density Richard L. Hansen and Joel M. Harris*

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

Lateral diffusion of a hydrophobic fluorescent molecule partitioned into monomeric alkyl chains bound to a planar silica substrate was measured as a function of chain density and chain length. Measurement of fluorescence recovery after patterned photobleaching was used to observe the diffusional relaxation of a concentration profile of probe molecules over distances of micrometers. The diffusion rate of the probe molecule partitioned into C-18 chains decreased with decreasing chain coverage. As the chain length was reduced from C-18 to C-8 and C-4, the rate of diffusion also decreased. These results, when combined with results from a previous study of the effect of overlaying solvent on diffusion rate (Hansen, R. L.; Harris, J. M. Anal. Chem. 1995, 67, 492-498), are consistent with a domain model for long-range transport of partitioned molecules through the bound ligands. Fluorescence recovery experiments in which diffusion is monitored over a distance of micrometers offer a unique means to probe long-range structure of surface-immobilized alkyl chains. The widespread utility of reversed-phase liquid chromatography (RPLC) has led to many studies to characterize the chemical nature of the RPLC environment. Several reviews that survey the studies of structure and dynamics of the RPLC bonded phase1-9 introduce the interested reader to the large body of literature on the subject. These reviews deal with bonding chemistry of RPLC alkyl ligands,1-6 characterization of the RPLC interphase,1-9 and development of retention models.1-5 Several reviews address spectroscopic characterization of the RPLC phase by optical techniques7,8 and NMR and ESR experiments.6,9 Researchers have investigated variations in experimental conditions such as mobilephase composition, chain length, and chain bonding density with the goal of optimizing separations and understanding the chemistry of the RPLC system. Studies examining the effect of chain length on RPLC systems have been both chromatographic and spectroscopic in nature. Chromatographic studies have shown that retention generally (1) Tijssen, R.; Schoenmakers, P. J.; Boehmer, M. R.; Koopal, L. K.; Billiet, H. A. H. J. Chromatogr. 1993, 656, 135-196. (2) Sander, L. C.; Wise, S. A. CRC Crit. Rev. Anal. Chem. 1987, 18, 299-415. (3) Gilpen, R. K. J. Chromatogr. Sci. 1984, 22, 371-377. (4) Dorsey, J. G.; Dill, K. A. Chem. Rev. 1989, 89, 331-346. (5) Dorsey, J. G.; Cooper, W. T. Anal. Chem. 1994, 66, 857A-867A. (6) Albert, K.; Bayer, E. J. Chromatogr. 1991, 544, 345-370. (7) Rutan, S. C.; Harris, J. M. J. Chromatogr., A 1993, 656, 197-215. (8) Wirth, M. J. LC-GC 1994, 12, 656-664. (9) Sentell, K. B. J. Chromatogr., A 1993, 656, 231-263. S0003-2700(96)00119-9 CCC: $12.00

© 1996 American Chemical Society

increases with increasing chain length,10-12 although selectivity may either increase or decrease, depending on the class of compounds being separated.13-16 NMR studies have shown that the mobility of alkyl chains decrease with increasing length, with the exception of a C-4 chain.17 Molecular dynamics simulations have recently predicted that, for a high coverage of alkyl ligands bound to silica, the motion of the ends of the attached chains is comparable for C-18 and C-8 ligands, with mobility of C-4 chains being much smaller.18,19 ESR studies with the small nitroxide probe TEMPO show an increase in probe dynamics in C-18 and C-8 layers compared with that in a C-4 layer.20 Similarly, a rotational dynamics study of a probe interacting with C-3, C-8, and C-18 surfaces found that the degree of anisotropy was largest for the C-3 surface and decreased with increasing chain length; as the rotational mobility of a probe increases, the anisotropy value decreases.21 Similarly, the effect of bonding density has also been investigated. Increasing the bonding density of monomeric C-18 alkyl ligands creates better shape selectivity in separations of polycyclic aromatic hydrocarbons (PAHs), but polymeric phases, which usually have higher coverages, generally have better selectivities.22-24 The retention of solutes in the RPLC interphase has been described by a mean field lattice theory by Dill and co-workers,25,26 which addresses the effects of chain bonding density. This theory describes the retention behavior for longchain phases as being predominately partitioning in nature. As the chain packing density increases, solutes will be more retained (10) Berendsen, G. E.; De Galan, L. J. Chromatogr. 1980, 196, 21-37. (11) Tanaka, N.; Sakagami, K.; Araki, M. J. Chromatogr. 1980, 199, 327-337. (12) Hennion, M. C.; Picard, C.; Caude, M. J. Chromatogr. 1978, 166, 21-35. (13) Sander, L. C.; Wise, S. A. Anal. Chem. 1987, 59, 2309-2313. (14) Hemetsberger, H.; Kellermann, M.; Ricken, H. Chromatographia 1977, 10, 726-730. (15) Krstulovic, A. M.; Colin, H.; Tchapla, A.; Guiochon, G. Chromatographia 1983, 17, 228-230. (16) Lochmu ¨ ller, C. H.; Wilder, D. R. J. Chromatogr. Sci. 1979, 17, 574-579. (17) Albert, K.; Pfleiderer, B.; Bayer, E. In Chemically Modified Oxide Surfaces (Chemically Modified Surfaces, Vol. 3); Leyden, D. E., Collins, W. T., Eds.; Gordon & Breach: New York, 1990; pp 233-243. (18) Yarovsky, I.; Aguilar, M.-I.; Hearn, M. T. W. Anal. Chem. 1995, 67, 21452153. (19) Ren, F. Ph.D. Thesis, University of Utah, Salt Lake City, UT, 1995; Chapter 5. (20) Reference 19, Chapter 4. (21) Rangnekar, V. M.; Foley, J. T.; Oldham, P. B. Appl. Spectrosc. 1992, 46, 827-831. (22) Wise, S. A.; May, W. E. Anal. Chem. 1983, 55, 1479-1485. (23) Wise, S. A.; Sander, L. C. J. High Resolut. Chromatogr. Chromatogr. Commun. 1985, 8, 248-255. (24) Sentell, K. B.; Dorsey, J. G. J. Chromatogr. 1989, 461, 193-207. (25) Marqusee, J. A.; Dill, K. A. J. Chem. Phys. 1986, 85, 434-444. (26) Dill, K. A. J. Phys. Chem. 1987, 91, 1980-1988.

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up to a maximum surface coverage, at which point entropic barriers due to chain ordering will cause solutes to be partially excluded; a reduction in retention at high surface coverages has been confirmed experimentally.27 The entropic barrier to partitioning at higher chain density causes solutes that can align with the alkyl chains to be more greatly retained; planar and rod-shaped solutes are retained more than comparable solutes having a larger volume.23,28 The better selectivity of polymeric phases, which often have higher chain densities than monomeric phases, may be simply due to increased chain ordering and not related to polymerization.23 Spectroscopic studies have also been used to investigate the effects of chain density on the RPLC interphase. NMR studies show an increased chain ordering with increasing chain density,29-31 inferred from a decrease in mobility along the alkyl chains. Molecular dynamics simulations have similar findings in that, with increasing chain density, the mobility of the alkyl chains decreases.18 EPR studies using two different spin probes found that the rotational mobilities of the probes decreased with increasing surface coverage.32 This study, along with others, has postulated the existence of at least two types of regions in the interphase due to aggregation or ordering of the alkyl chains.32-35 This effect is especially pronounced against a nonwetting solvent such as water,33 where the chains have been shown to collapse nearly into the plane of the substrate.36 The resulting surface may consist of regions of higher alkyl chain density, where the chains are more ordered, interspersed with regions of lower density, where the chains have a higher mobility. Most spectroscopic investigations designed to measure the mobility of a solute in an RPLC interphase involve fast relaxation motions of the probe20,21,32,34,36 or short-range movement of the probe;37-39 the mobility of the probe can be used to infer the dynamics of the interphase. Long-range diffusion studies, in which diffusion of a probe molecule is observed over distances of micrometers, may allow a unique insight into larger scale structures in the stationary-phase environment. Previous work utilizing a fluorescence recovery after patterned photobleaching (FRAPP) experiment has demonstrated variations in mobilities of probes that are adsorbed to the C-18/solution interface40 versus those of probes that are fully partitioned into C-18 chains.41 In the present study, the effect of chain length and chain density on rates of lateral diffusion of a hydrophobic probe partitioned into alkyl ligands is examined. A FRAPP experiment was used to (27) Sentell, K. B.; Dorsey, J. G. Anal. Chem. 1989, 61, 930-934. (28) Sentell, K. B.; Henderson, A. N. Anal. Chim. Acta 1991, 246, 139-149. (29) Albert, K.; Evers, B.; Bayer, E. J. Magn. Reson. 1985, 62, 428-436. (30) Bayer, E.; Paulus, A.; Peters, B.; Laupp, G.; Reiners, J.; Albert, K. J. Chromatogr. 1986, 364, 25-37. (31) Gilpen, R. K.; Gangoda, M. E. Anal. Chem. 1984, 56, 1470-1473. (32) Wright, P. B.; Lamb, E.; Dorsey, J. G.; Kooser, R. G. Anal. Chem. 1992, 64, 785-789. (33) Zeigler, R. C.; Maciel, G. E. J. Am. Chem. Soc. 1991, 113, 6349-6358. (34) Miller, C.; Joo, C.; Roh, S.; Gorse, J.; Kooser, R. G. In Chemically Modified Oxide Surfaces (Chemically Modified Surfaces, Vol. 3); Leydon, D. E., Collins, W. T., Eds.; Gordon & Breach: New York, 1990; pp 251-268. (35) Lochmu ¨ ller, C. H.; Colborn, A. S.; Hunnicutt, M. L.; Harris, J. M. J. Am. Chem. Soc. 1984, 106, 4077-4082. (36) Montgomery, M. E., Jr.; Green, M. A.; Wirth, M. J. Anal. Chem. 1992, 64, 1170-1175. (37) Bogar, R. G.; Thomas, J. C.; Callis, J. B. Anal. Chem. 1984, 56, 10801084. (38) Ståhlberg, J.; Almgren, M.; Alsins, J. Anal. Chem. 1988, 60, 2487-2493. (39) Wong, A. L.; Harris, J. M. J. Phys. Chem. 1991, 95, 5895-5901. (40) Zulli, S. L.; Kovaleski, J. M.; Zhu, X. R.; Harris, J. M.; Wirth, M. J. Anal. Chem. 1994, 66, 1708-1712. (41) Hansen, R. L.; Harris, J. M. Anal. Chem. 1995, 67, 492-498.

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measure diffusion of a probe partitioned into three coverages of C-18 ligands and in a C-8 and C-4 layer. A FRAPP experiment consists of rapidly photobleaching an initially homogeneous distribution of fluorophores with an illumination pattern that is spatially periodic, thereby creating a periodic concentration profile. Following photobleaching, fluorescence emission is monitored as the concentration profile is probed with the same illumination pattern, reduced in intensity to minimize further photobleaching. As the concentration profile relaxes by diffusion, the net movement of fluorophores from nonilluminated (unbleached) regions into the illuminated regions produces a fluorescence recovery. The temporal response of the fluorescence signal can be used to determine the diffusion coefficient of the fluorophore. In this experiment, the periodic excitation profile was created by interfering two coherent laser beams at an n-alkyl-modified silica/solution interface within a flow cell; a fluorophore was contained within the alkyl chains on the silica substrate. Excitation was confined to the silica/solution interface by total internal reflection (TIR), and the excitation profile created by the ppolarized laser beams is described by42

df )

(λo/n1) 2 sin θ sin φ

(1)

where the fringe spacing df is dependent on (λo/n1), the wavelength of light in the higher index of refraction material from which the beams internally reflect, θ, the angle of incidence, and φ, the angle the interfering beams make with their bisector. If the degree of photobleaching is small, the diffusional recovery is expected to be single-exponential, in which τr, the time constant of the recovery, contains the diffusion coefficient D:42,43

τr ) df2/4π2D

(2)

D varies with the square of the fringe spacing; therefore, plotting the recovery rate against the inverse square of the fringe spacing allows the diffusion coefficient to be determined from the slope of a best fit line. The probe used in this study was rubrene, a tetracene derivative with phenyl groups attached to the 5, 6, 11, and 12 positions. Rubrene is very hydrophobic and partitions into the alkyl ligands of a C-18 surface; mercuric chloride, which is not retained in a C-18 layer, was unable to quench rubrene partitioned into C-18 ligands in contact with water.41 Rubrene photooxidizes easily and controllably to form a stable endoperoxide product under moderate laser intensities;44 the endoperoxide product has no visible absorption, making rubrene an ideal probe for this study. EXPERIMENTAL SECTION Sample Preparation. Fused silica microscope slides (ESCO R330110) were cleaned for approximately 30 min in a hot acid bath consisting of a 1:1 ratio by volume of concentrated nitric and sulfuric acids. This process removed any covalently bound alkyl chains from previously used slides and any organic material from (42) Abney, J. R.; Scalettar, B. A.; Thompson, N. L. Biophys. J. 1992, 61, 542552. (43) Davoust, J.; Devaux, P. F.; Leger, L. EMBO J. 1982, 1, 1233-1238. (44) Ernsting, N. P.; Schmidt, R.; Brauer, H.-D. J. Phys. Chem. 1990, 94, 52525255.

Table 1. Quantity of Silane Reagents Used To Create C-18, C-8, and C-4 Slides with Corresponding Advancing and Receding Contact Angles contact angle (deg) reagent

amount (g)

octadecyldimethylchlorosilane >0.1 6.0 × 10-4 2.3 × 10-5 octyldimethylchlorosilane >0.1 butyldimethylchlorosilane >0.1

advancing

receding

97.2 ( 0.5 67.9 ( 0.7 80.1 ( 0.4 43.3 ( 1.0 57.4 ( 0.8 ∼0 93.6 ( 0.2 64.3 ( 1.0 94.8 ( 1.4 78.7 ( 0.3

unused slides. Following thorough rinsing with glass-distilled and deionized (17.9 MΩ) water, the slides were sonicated for 5 min in a 1:1 mixture of ammonium hydroxide and water, rinsed further with glass-distilled and deionized water, and placed in an oven to dry at 130 °C. Monochlorosilane reagents (Hu¨ls) were reacted with silanol groups on the silica surface by refluxing for 12 h in 250 mL of toluene previously dried over 3 Å molecular sieves. Five milliliters of pyridine was added as a catalyst, and the reaction was run under an atmosphere of nitrogen. Following derivatization, the slides were cleaned in tetrahydrofuran (THF) and stored under methanol. The bonded C-18 ligand density was controlled by the amount of silane reagent added to the reaction mixture as shown in Table 1. C-8 and C-4 surfaces were prepared according to the same procedure as that described above. Contact Angle Measurements. Contact angles were measured with a Wilhelmy-Balance apparatus constructed in-house at the University of Utah Department of Bioengineering; results are reported in Table 1. Slides were dipped into 18 MΩ water at a rate of 2.35 cm/min, while a balance measured the force, F, imparted to the slide from gravity, wetting phenomena, and buoyancy forces. These forces are related by the equation

F ) mg + PγLV cos(θ) - FB

(3)

where mg is a gravitational force, P is the perimeter distance of the slide, γLV is the surface tension of water, θ is the contact angle, and FB is a buoyant force from the column of water under the slide.45 The contact angle at zero immersion, where the contribution from buoyant forces is zero, is calculated by extrapolating the immersing and withdrawing traces to the point of contact between the slide and water. Figure 1 is an example of data acquired from a Wilhelmy-Balance experiment on a C-4 slide. The advancing and receding slopes were fit in QuatroPro to a straight line by linear regression, and the intercept values were used to calculate the force at zero immersion. Diffusion Measurements. Diffusion measurements were made with an experimental procedure and setup described in detail previously,41 with two changes: the excitation source was replaced by a Coherent Inova-K krypton ion laser operating at 530.9 nm, and data collection was accomplished by gated photon counting as follows. The signal from the collection PMT (Hamamatsu R928) was amplified with a 300 MHz bipolar amplifier (Phillips Scientific) and counted with a multichannel scaler (EG&G Ortec TurboMCS). (45) Andrade, J. D.; Smith, L. M.; Gregonis, D. E. In Surface and Interfacial Aspects of Biomedical Polymers, Vol. 1; Andrade, J. D., Ed.; Plenum: New York, 1985; pp 249-292.

Figure 1. Wilhelmy-Balance data taken on a fused silica substrate modified with C-4 ligands. The immersion rate was 2.35 cm/min. Extrapolation of the immersing and withdrawing traces to zero immersion depth allows the force imparted to the slide from wetting phenomena to be calculated and the contact angle found (see text). Advancing and receding contact angles for this surface were θadv ) 92.6° and θrec ) 77.5°, respectively.

Figure 2. Fluorescence recovery transient and resulting singleexponential fit from diffusion of rubrene on a C-8 surface. The time constant of the fit was 9.09 s.

A rubrene solution was brought into contact with a derivatized fused silica microscope slide in a flow cell and allowed to equilibrate with the surface. The dye concentration was 30 µM in a 60:40 mixture of water and THF containing no peroxide inhibitor. This concentration and solvent mixture were chosen to keep the partitioned dye coverage at ∼1% of a monolayer.41 Following removal of the dye solution, the cell was flushed several times with an 80:20 (by volume) water/methanol mixture and eventually filled with this solution; all diffusion measurements were made against this water/methanol solution. FRAPP experiments were conducted by recording four recovery transients taken on different areas of the sample and averaging within the photon counter software; data were fit in a similar fashion to a single-exponential function as previously described.41 An example recovery transient and resulting fit of diffusion of rubrene at a C-8 interface are shown in Figure 2. Fitting five such averages for a given fringe spacing at five separate fringe spacings for an experiment and combining results produced a plot such as that seen in Figure 3. The diffusion coefficient was calculated from the slope of the line (see eq 2) derived from a weighted least-squares fit of the data. Each experiment was repeated in triplicate and combined in a weighted average. RESULTS Contact Angle Results. Contact angles were measured by a Wilhelmy-Balance experiment, allowing for measurement of both advancing and receding contact angles. The immersion rate of 2.35 cm/min was within the range found to be free of speed effects Analytical Chemistry, Vol. 68, No. 17, September 1, 1996

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Figure 3. Weighted fit of recovery rate, 1/τr, versus the inverse square of the fringe spacing, 1/df2, for rubrene diffusing on a C-8 surface. The diffusion coefficient is calculated from the slope of the line (see eq 2).

for a similar experiment.46 Silica surfaces modified by covalently binding C-18 alkyl ligands were produced in this study by reducing the concentration of octadecyldimethylchlorosilane in the reaction flask. At lower chain bonding densities, the surface will behave more like a fused silica substrate, producing a low contact angle. At higher chain bonding densities, the surface will have a more hydrophobic character and higher contact angle. C-18 slides derivatized with decreasing amounts of reagent were found to have increasingly smaller contact angles. The advancing angles decreased from θadv ) 97.2° to 80.1° to 57.4°, as seen in Table 1. Over this range, however, the receding angles decreased from approximately θrec ) 67.9° to 43.3° to 0°; the greater hysteresis for lower coverages suggests a greater surface inhomogeneity,47,48 possibly caused by aggregation of the alkyl chains.49 Contact angles for heterogeneous surfaces consisting of two or more distinct chemical species are difficult to interpret but are related to the chemical nature and amount of each surface species. Theories predicting contact angles for heterogeneous surfaces, such as that developed by Cassie and Baxter50 or, in cases when the surface heterogeneity approaches molecular scales, by Israelachvili and Gee,47 are based on each chemically unique species contributing to the collective surface properties based on a population fraction. It is reasonable to characterize the surfaces used in this study by contact angle experiments; systematic changes in the relative amounts of a surface species can be followed by monitoring changes in contact angles. A population fraction of alkyl chains can be calculated by using the theory developed by Israelachvili et al. presented in eq 4.

(1 + cos θ)2 ) f1(1 + cos θ1)2 + f2(1 + cos θ2)2

(4)

Although this equation does not directly calculate surface bonding densities of the alkyl ligands, it does predict a population fraction of surface species and can be used to illustrate a declining alkyl ligand surface fraction with decreasing concentration of the ligand reagent in the surface binding reaction. If we assume a contact angle of θalkyl ) 112° 51 and θsilica ) 0°, we can calculate the fractional coverage, falkyl, of alkyl ligands by utilizing the experimentally measured advancing contact angles. For C-18-derivatized (46) Park, J.-M.; Kim, J. H. J. Colloid Interface Sci. 1994, 168, 103-110. (47) Israelachvili, J. N.; Gee, M. L. Langmuir 1989, 5, 288-289. (48) Schwartz, L. W.; Garoff, S. Langmuir 1985, 1, 219-230. (49) Lin, Y.-S.; Hlady, V. Colloids Surf. B 1994, 2, 481-491. (50) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546-551. (51) Ulman, A. J. Mater. Educ. 1989, 11, 205-279.

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Figure 4. Diffusion coefficients of rubrene on C-18-derivatized surfaces versus their water contact angle. Rubrene diffusion was measured against an 80:20 (by volume) water/methanol solution. Error bars indicate the 95% confidence limits.

slides, the fractional alkyl coverage decreases with decreasing contact angle; percent coverages were calculated to be falkyl ) 90%, 73%, and 45% for advancing contact angles of θadv ) 97.2°, 80.1°, and 57.4°, respectively. These coverage estimates are higher by 10% than those derived from the Cassie equation,50 which simply assumes additivity of contact angle contributions. Although the fractional coverages are uncertain due to the state of theory in contact angle interpretation, they clearly indicate that the fraction of bound ligands on the surface is influenced by the reaction conditions. This variation, although not under strict quantitative control, provides justification for interpreting the influence of ligand coverage on the surface diffusion rate of rubrene. Contact angle experiments were also performed on derivatized surfaces of C-8 and C-4 ligands. Both C-8 and C-4 surfaces were derivatized in a manner consistent with the high-coverage C-18 slide, and measured contact angles of θadv ) 93.6° and 94.8° confirm high coverage. The receding angle measured for the C-4 surface was θrec ) 78.7°, indicating a smaller degree in bonding heterogeneity than for the high-coverage C-18 surface and the C-8 surface, with receding contact angles of θrec ) 67.9° and 64.3°, respectively. Lateral Diffusion Results. Lateral diffusion of rubrene, a hydrophobic probe that partitions into the alkyl chains of a RPLC interphase, was measured by a FRAPP experiment as previously described.41 For the three coverages of monomeric C-18 ligands, it was found that the rate of rubrene diffusion decreased with decreasing surface coverage. Diffusion coefficients of D ) (4.0 ( 0.4) × 10-9, (3.3 ( 0.5) × 10-9, and (2.9 ( 0.4) × 10-9 cm2/s were measured and plotted in Figure 4 for C-18 slides with advancing contact angles of θadv ) 97.2°, 80.1°, and 57.4°, respectively; the error bounds indicate the 95% confidence limit. While the diffusion coefficient measured on the intermediate C-18 coverage (θadv ) 80.1°) is statistically indistinguishable from that on the high- and low-coverage surfaces at the 95% confidence limit, the diffusion coefficients on the high and low coverage slides (θadv ) 97.2° and 57.4°, respectively) are distinguishable. It can be inferred from these results that the trend is a decreasing diffusion rate with decreasing surface coverage. Previously, diffusion of rubrene partitioned into C-18 ligands on a planar substrate against an identical aqueous phase as used in this experiment was measured to be D ) (2.8 ( 0.4) × 10-9 cm2/s.41 Although it was thought that the ligand coverage of the previously used slide was high, unfortunately, contact angle measurements were never taken to test the coverage of C-18 ligands. The diffusion rate is indistinguishable from that of the

Figure 5. Diffusion coefficients of rubrene on high-coverage alkylated silica surfaces versus alkyl chain length. Rubrene diffusion measured against an 80:20 (by volume) water/methanol solution. Error bars indicate the 95% confidence limits.

intermediate coverage slide and may indicate that the previous slide did not have as high a coverage as that of the high-coverage slide used in this study. These results point out the need to control alkyl ligand coverage in these experiments. Diffusion of rubrene was also measured on slides derivatized with monomeric C-8 and C-4 ligands. The C-8 and C-4 slides had advancing contact angles of θadv ) 93.6° and 94.8°, respectively, compared with the high-coverage C-18 slide, with θadv ) 97.2°. Figure 5 summarizes the measured diffusion coefficients for the three chain lengths, which decreased with decreasing chain length, from D ) (4.0 ( 0.4) × 10-9 to (2.5 ( 0.3) × 10-9 to (2.4 ( 0.3) × 10-9 cm2/s for surfaces derivatized with C-18, C-8, and C-4 ligands respectively; error bounds indicate the 95% confidence limits. Diffusion coefficients on the C-8 and C-4 surfaces were indistinguishable at 1 standard deviation but were clearly distinguishable from diffusion on the C-18 surface. DISCUSSION In an effort to better understand long-range diffusion of rubrene in a RPLC interphase, the ligand coverage and chain length influences were investigated. In previous work, it was found that the rate of diffusion of rubrene in a C-18 layer increased with increasing methanol content in the overlaying solvent; diffusion coefficients of D ) (1.5 ( 0.2) × 10-9, (2.1 ( 0.3) × 10-9, and (2.8 ( 0.4) × 10-9 cm2/s for 0%, 10%, and 20% methanol in aqueous solution, respectively, were measured. The increase in the diffusion coefficients with increasing methanol in the overlaying solvent was thought to be caused by an increase in chain mobility as the interphase volume increased; methanol in the overlaying solution reduced the surface tension at the alkyl chain/solution interface, reducing the drive for the alkyl chains to collapse against water to minimize contact area. Two previous studies have examined lateral diffusion of pyrene, another hydrophobic polycyclic aromatic hydrocarbon, partitioned into C-18 ligands bound to porous silica gel;37,38 similar to rubrene, pyrene has been shown to partition into C-18 chains against an aqueous solution.52 Diffusion coefficients for pyrene were measured by an excimer formation experiment that operates on a 107fold faster time scale than the FRAPP experiment. Against a 75: 25 methanol/water overlaying solvent, a diffusion coefficient of D ) 2.5 × 10-7 cm2/s was calculated from the ratio of monomer to excimer emission.37 Against water with a small amount of sodium tetradecyl sulfate surfactant present,38 the diffusion coef(52) Carr, J. W.; Harris, J. M. Anal. Chem. 1987, 59, 2546-2550.

ficient was determined to be D ) 9 × 10-8 cm2/s.40 Since diffusion is measured by excimer formation, and therefore only during the lifetime of the excited state (∼100 ns), the distance over which the probe could travel was of the order of 20 Å. In an effort to rationalize the nearly 2 order of magnitude discrepancy between our results and those for pyrene, we postulated in a previous work both probe-molecule size and experimental distance-scale factors as possible origins of observed differences.41 An additional source of observed difference may arise from the organization of alkyl ligands bound to porous silica gel as compared to a flat surface as used in this study. Rotational diffusion dynamics studies have shown probe size effects in longchain alkane and alcohol solvents;53,54 when the solute is large compared with the size of the solvent, rotational diffusion occurs near the hydrodynamic stick limit. As the solute molecule decreases in size, however, a change to the slip limit is observed. Pyrene diffusion within the C-18 layer may be more sliplike in character than rubrene. Second, it is likely that the curvature of the substrate surface influences the organization of the bound alkyl ligands.55 The differences in interligand contact in convex and concave regions of a porous substrate could create a more heterogeneous environment with respect to chain density compared to that of similar chain coverages on a flat surface. Pyrene molecules may concentrate into hydrophobic regions on the derivatized porous silica gel,52 making the diffusion coefficient calculated by an excimer formation experiment high. Although molecular size and substrate curvature factors may play a role in the discrepancy in measured diffusion rates, it is unlikely that 2 orders of magnitude can be explained by these effects alone. Finally, it was proposed that the large differences in distance scales of the diffusion experiments may play a role in the observed diffusion rates.41 Because the pyrene experiments measured diffusion over ∼20 Å, the local motion sampled in these experiments may be different than the long-range motion (diffusion over micrometers) sampled in the FRAPP experiment. Inhomogeneities in surface binding density have been observed for silane reagents,35 and, coupled with the observation that against an aqueous phase, the chains collapse lying nearly in the plane of the substrate,36 a distribution of sorption domains (consisting of regions of locally higher alkyl density) may exist on the surface.33 A hydrophobic molecule would preferentially partition into such domains. Barriers to long-range diffusion of rubrene over the surface may be due to movement of the probe from one domain to another or the slow motion of the domains themselves. These domains could be in part responsible for “roughness features” described by Wirth et al.40,56 to account for hindered in-plane reorientation and fast in-plane rotation of a non-partitioned probe at a C-18/water interface, together with a slow lateral diffusion rate. The ligand coverage and chain length influences on the diffusion rate of rubrene presented are considered in light of this long-range diffusion model. It is proposed that the rate of longrange diffusion is controlled by movement of the probe molecule between sorption domains or by the movement of domains themselves. For molecules to move between domains, it is necessary for the probe to be exposed to a more polar environment. Given the hydrophobic nature of the probe, it is expected (53) Ben-Amotz, D.; Drake, J. M. J. Chem. Phys. 1988, 89, 1019-1029. (54) Jiang, Y.; Blanchard, G. J. J. Phys. Chem. 1994, 98, 6436-6440. (55) Avnir, D. J. Am. Chem. Soc. 1987, 109, 2931-2938. (56) Wirth, M. J.; Burbage, J. D. J. Phys. Chem. 1992, 96, 9022-9025.

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that such a step would be costly in free energy. Long-range diffusion, if controlled by movement of sorption domains across the surface, would be expected to increase upon increasing chain mobility. In the previous study,41 we noted an increase in rubrene diffusion with increasing methanol in the overlaying aqueous solution; organic modifiers added to overlaying aqueous solutions are retained at the alkyl chain/solution interface57 and have been shown to increase the chain mobility.29,30 An increase in chain mobility may correlate with an increase in local probe movement, as seen when comparing short-range experiments. With increasing alkyl chain coverage, EPR experiments demonstrated an increase in local chain order calculated from the reduced rotational mobility of two separate probes.32 In the pyrene excimer experiments, faster diffusion was found against the mobile phase containing methanol37 versus water with a small amount of surfactant.38 However, it has been shown that chain mobility decreases with increasing chain density18,29-31 as the chains become more ordered; contrary to the short-range diffusion experiments, the long-range diffusion of rubrene is not aided by an increase in chain mobility. Rather, the volume of the interphase increases both with increasing methanol content36 and with increasing chain density.58 Increasing the volume of the interphase may help reduce regions energetically unfavorable to the probe by increasing the continuity of the alkyl chain interphase. The rate of diffusion was also found to decrease with decreasing chain length. With the exception of a C-4 surface, NMR results indicate that overall chain mobility decreases with increasing chain length.17 This evidence is again contradictory with the notion that chain mobility is responsible for the rate of long-range diffusion of a partitioned probe. Retention of hydrophobic probes on alkyl chains of varying lengths increases with increasing chain length up to a “critical” length, which depends on the size of the solute. For example, against an 80:20 methanol/water mobile phase, the critical chain lengths for naphthalene and anthracene are 10.9 and 12.2 carbons, respectively.10 Rubrene is larger than both of these molecules and would, therefore, have a correspondingly larger critical chain length. Solubility of a solute within the stationary phase can be improved by increasing the alkyl chain length for chains shorter than the critical length. Above the critical chain length, the stationary phase can only slightly better solvate the solute by increasing interphase thickness. Rubrene is able to partition into the C-4 and C-8 surfaces to some extent, although these chain lengths are below the critical length for a molecule as large as rubrene. Evidence for this comes when comparing the long-range diffusion rate of rubrene with acridine orange, a probe that sorbs to the alkyl chain/solution interface rather than fully partitioning into the alkyl ligands.59 Rubrene diffuses approximately 2 orders of magnitude more slowly than acridine orange on a C-18 surface under identical experimental conditions.40,41 The diffusion rate of rubrene does not increase to that measured for acridine orange on the short(57) McCormick, R. M.; Karger, B. L. Anal. Chem. 1980, 52, 2249-2257. (58) Sander, L. C.; Glinka, C. J.; Wise, S. A. Anal. Chem. 1990, 62, 1099-1101. (59) Wirth, M. J.; Burbage, J. D. Anal. Chem. 1991, 63, 1311-1317. (60) Sun, Y.-P.; Ma, B.; Lawson, G. E.; Bunker, C. E.; Rollins, H. W. Anal. Chim. Acta, in press.

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chain surfaces, indicating some degree of entanglement even with the shorter phases. Rubrene appears to experience some partitioning on the shorter phases, but because of its large size it may be confined to a region closer to the substrate as compared to partitioning into the C-18 phase. Such a restriction may lead to a reduction in observed diffusion rates on the C-4 and C-8 surfaces as compared with that on the C-18 surface. An interphase created by longer chains creates an environment in which movement of the probe is less hindered. It is interesting that the C-8 and C-4 results are not more dramatically different. Perhaps the C-4 coverage used in this experiment was higher and more uniform than that of the C-8 slide, creating surfaces similar in continuity as probed by rubrene. Contact angle measurements indicated that the C-4 surface was the most homogeneous from the small hysteresis between advancing and receding angles. The C-4 surface used would not have partitioned rubrene as completely as the C-8 surface, but the homogeneity of the surface may have lowered barriers to long-range diffusion, consistent with diffusion in a domain model. To fully rationalize the discrepancy in diffusion results between pyrene and rubrene, a long-range diffusion experiment involving pyrene as the probe would be ideal. This was attempted by a FRAPP experiment, with the unfortunate result that pyrene did not behave well photophysically.60 The experiment was also attempted with other partitioning probes with photochemistry similar to that of rubrene, such as 9,10-diphenylanthracene, which were found to be highly temperature sensitive. The amount of UV light required to photobleach such fluorophores also heated the interface and was difficult to characterize; the probes relax at higher temperatures more efficiently by nonradiative means, giving the unfortunate appearance of a photobleaching response with a rapid (fringe-spacing independent) recovery. CONCLUSION Long-range diffusion of rubrene partitioned into the monomeric alkyl chains on silica has been measured. It was found that the diffusion coefficient decreased with decreasing coverage of C-18 ligands and decreased with decreasing chain length (C-8 and C-4 surfaces). The results are consistent with a long-range diffusion model whereby the hydrophobic solute moves through regions of varying alkyl chain density over the surface. Conditions that favor a more continuous interphase such as contact with overlaying solvents containing an organic modifier, greater chain densities, and longer alkyl chains, minimize the regions energetically unfavorable for the probe to pass through. As a result, the rate of diffusion increases with increasing interphase continuity. ACKNOWLEDGMENT This research was supported in part by the U.S. Department of Energy. Additional fellowship support from Pfizer (to R.L.H.) is gratefully acknowledged. Received for review February 5, 1996. Accepted May 13, 1996.X AC960119J X

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