Anal. Chem. 1996,67,492-498
Lateral Diffusion of Molecules Partitioned into C-I 8 Ligands on Silica Surfaces Richard L. Hansen and Joel M. Had$* Department of Chemistry, Univetsity of Utah, Salt Lake City, Utah 841 12
Lateral diffusion rates of a fluorescent probe molecule partitioned into chromatographic (2-18 ligands on a planar silica substratewere measured as a function of overlaying solvent composition. Diffusion coefficients of the probe were measured with a fluorescence recovery after patterned photobleaching experiment. A total internal reflection fluorescence flow cell held the derivatized planar substrate in contact with various aqueous solutions and allowed the fluorescence signal from two interfering, total internally reflected laser beams to be imaged onto a detector. DifFusion coefficientsfor the partitioned probe were -3 orders of magnitude smaller than a s i o n in solution and were found to increase with increasing methanol concentration in the overlaying aqueous solvent mixture. Inability of a solution phase ionic quencher to quench the fluorescence of sorbed rubrene con6rmed that the probe is fully partitioned into the C-18 chains.
For the past 20 years, the use of modified silicas in reversed phase chromatography in HPLC separations has steadily increased. During this time period, research has focused on probing and characterizing the interfacial chemistry of these materials' with a wide variety of spectroscopic technique^.*-^ For example, NMR measurements have been used to probe chain dynamics and solvent/chain interaction~.~~~-~ FT-IR experiments were used to study alkyl chain conformations in C-18 layers? Other optical methods using electronic excitation of probe molecules have been exploited including photoacoustic and reflectance spectroscopies2J0J1and fluorescence-based experiments.2A12-16 Studies characterizing the alkyl chains bound to silica can be used to create a picture of the C-18 interfacial environment. Monomeric alkyl chains bound to silica possess a degree of Dorsey, J. G.; Cooper, W. T. Anal. Chem. 1994,66,857.4. Rutan, S. C.; Harris, J. M. J. Chromatrogr. A 1993,656,197. Sentell, K. B. J. Chromatogr. A 1993,656,231. Wirth, M. J. LC-GC 1994,12,656. Sindorf, D. W.; Maciel, G. E. J. Am. Chem. SOC. 1983,105, 1848. Gilpin, R K.; Gangoda, M. E. Anal. Chem. 1984,56,1470. (7) Marshall, D. B.; McKenna, W. P. Anal. Chem. 1984,56, 2090. (8) Bliesner, D. M.; Sentell, K. B. Anal. Chem. 1993,65, 1819. (9) Sander, L. C.; Callis, J. B.; Field, L. R Anal. Chem. 1983,55, 1068. (10) Lochmtiller, C. H.; Marshall, S. F.; Wilder, D. R Anal. Chem. 1980,52, 19. (11) Jones, J. L.; Rutan, S. C. Anal. Chem. 1991,63,1318. (12) StAhlberg, J.; Almgren, M. Anal. Chem. 1985,57, 817. (13) Carr, J. W.; Harris, J. M. Anal. Chem. 1987,59, 2546. (14) Wong, A L.;Hunnicutt, M. L.; Harris, J. M. Anal. Chem. 1991,63,1076. (15) Wirth, M. J.; Burbage, J. D. Anal. Chem. 1991,63,1311. (16) Montgomery, M. E., Jr.; Green, M. A ; Wirth, M. J. Anal. Chem. 1992,64, 1170. (1) (2) (3) (4) (5) (6)
492 Analytical Chemistry, Vol. 67,No. 3, February 1, 1995
conformational disorder. When in contact with a water/methanol solution, the chains exhibit less conformationaldisorder than the corresponding n-alkane l i q ~ i d .Bound ~ alkyl chains also possess a degree of mobility that increases up to the ninth carbon position from the silica substrate.5J7 Even at the highest bonding densities achievable with monomeric silane reagents, alkyl ligands have suf6cient room to tilt and rotate and possess kinks and bends. Maximum bonding densities of octadecyldimethylsilanereagents on silica surfaces are 3-4pmol m-2 l8 with typical coverages being somewhat smaller. This coverage corresponds to 40-60 k per chain. A closepacked and ordered saturated alkyl chain requires -20 A2of surface area,lgsome 2-3 times less space than afforded it on a silica surface. Maximum surface coverage is controlled by steric effects arising from methyl groups on the silane reagent. The relatively looser packing of the alkyl chains makes the chromatographicreversed phase environment different from that of self-assembled monolayers or Langmuir-Blodgett films! Any discussion of the reversed phase chromatographic surface environment is incomplete without consideration of the overlaying solvent.' As the composition of the solvent is altered, the thickness and character of the (2-18 layer changes. In the presence of pure water, the chains collapse, reducing the layer thickness to minimize the area of the alkyl ligand/water interface; under these conditions, evidence exists that the chains lie nearly in the plane of the silica substrate.16.20If an organic modfier such as methanol is added to the water, even in small amounts, the modifier is retained at the interface, enriching the (2-18 layer.21%22 As retention of the organic modilier occurs, the layer thickness increases and the chains become more extended.13 This effect is seen most strongly for long-chain alcohols16 but also occurs for methan01.l~Alcohols are amphiphilic, and their surfaceexcess concentrations can lower the interfacial tension between the hydrophobic surface and the overlaying aqueous solvent. More efficient wetting of the interface reduces the drive to minimize the alkyl chain surface area. In addition to causing the C-18 layer to swell, intercalation of methanol also changes the polarity of the phase. This phenomenon has been studied with sorbed fluorescent probe m01ecules'~J~~~~ and covalently bound probe^.^*,^^ (17) Bayer, E.; Paulus, A ; Peters, B.; Laupp, G.; Reiners, J.; Albert, K. J. Chromatogr. 1986,364,25. (18) Hemetsberger, H.; Behrensmeyer, P.; Henning, J.; Ricken, H. Chromatographia 1979,12, 71. (19) Gennis, R B. Biomembranes; Molecular Structure and Function; Cantor, C. R, Ed.; Springer-Verlag: New York, 1989. (20) Montgomery, M. E., Jr.; Wirth, M. J. Anal. Chem. 1994,66,680. (21) McCormick, R M.; Karger, B. L. Anal. Chem. 1980,52,2249. (22) Scott, R P. W.; Simpson, C. F. Faraday Symp. Chem. SOC. 1980,15,69. (23) Men, Y.; Marshall, D. B. Anal. Chem. 1990,62,2606. (24) Lochmiiller, C. H.; Marshall, D. B.; Wilder, D. R Anal. Chim. Acta 1981, 130,31. 0003-2700/95/0367-0492$9.00/0 0 1995 American Chemical Society
As the nature of the C-18 layer is altered by varying the overlaying solvent composition, the interfacial environment of a sorbed probe molecule also changes. In addition to polarity changes within the phase, chain dynamics are af€ected by the surrounding en~ironment.1~ Chain mobility would be expected to increase with increasing organic modifier concentration. The alkyl chain dynamics can be indirectly probed by following the movement of a probe molecule residing within the C-18 layer. In this paper, the diffusion rate of a fluorescent probe partitioned into the C-18 layer is measured in the presence of several overlaying solvent compositions. Changes in the interfacial mobility of the probe are correlated with changes in chain dynamics. A planar silica substrate was used to support a C-18 layer in which diffusion of a fluorescent probe molecule, rubrene, was measured. Rubrene is an eight-ring polycyclic aromatic hydrocarbon that is hydrophobic and strongly partitions into a C-18 layer under the conditions of this experiment. Diffusion coefficients were measured by fluorescence recovery after patterned photobleaching (FRAF'P) 125 which was recently adapted to studies of diffusion of molecules at chromatographic silica/solution interfaces.26 A FRAPP experiment utilizes a spatially periodic excitation pattern to photobleach a concentration profile in a homogeneous distribution of fluorophores. The resulting periodic concentration profile relaxes due to the diffusion of molecules in the concentration gradient. If the profile is illuminated with the same excitation pattern used for photobleaching (only greatly attenuated to avoid further photochemistry), the relaxation of the concentration gradient can be monitored. As fluorophores diffuse from regions of high concentration corresponding to nonilluminated areas into regions of low concentration corresponding to illuminated areas, the fluorescence signal increases. The temporal response of the fluorescence recovery can be used to determine the diffusion coefficient of the fluorophore. The spatially periodic photobleaching and probing patterns used in this experiment were created by interferingtwo coherent laser beams at the C-l8/solution interface within a total internal reflection fluorescence (TIRF) flow cell. The resulting interference pattern, created by the superposition of electric fields from two laser beams oscillating perpendicular to the plane of the interface, is sinusoidal27with a fringe spacing, 4, given by
that depends on (;Z,,/nd, the wavelength of light in the high refractive index material from which the beams internally reflect, 8, the angle of incidence, and 4, the angle the intersecting beams make with their bisector. If the degree of photobleaching is the concentration profiles created by the excitation pulse will also be sinusoidal. Under these conditions, the expected fluorescence recovery is a single exponential in which the time constant for the recovery depends on the square of the fringe spacing and inversely on the diffusion coefficient, D:25,27 z, = d,2/42D
(2)
Determining the fringe spacing from the angles that the excitation beams intersect at the interface, and fitting the (25) Davoust, J.; Devaux, P. F.; Leger, L. EMBOJ. 1982, 1,1233. (26) Zulli, S. L.; Kovaleski, J. M.; Zhu, X. R;Harris, J. M.; Wirth, M. J. Anal. Chem. 1994, 66, 1708. (27) Abney, J. R; Scalettar, B. A; Thompson, N. L. Biophys. I. 1992,61,542.
4 Laser
I'
(Sideview)
'\,
Figure 1. Diagram of the FRAPP experiment. See text for description. The two insets show the mirrors that rotate the beams (side view) and the TIRF flow cell; the latter supports a C-18 derivatized silica slide for collection of fluorescence recovery transients.
fluorescence recovery to obtain z, one can determine the diffusion coefficient of the fluorescent probe on the surface. EXPERIMENTAL SECTION
Diffusion Measurements. The experimental layout for the FRAPP diffusion measurements is shown in Figure 1. An argon ion laser (Spectra Physics, Model 165) operated at 488 nm was used as the excitation source. The laser beam was propagated through a set of matched optical flats OF1 and OF2 in which the internal reflections were used to create a weak probe beam. The probe beam could be aligned to coincide with the stronger excitation beam transmitted through the optical flats by changing the relative angles of the flats.28 A shutter S1 (Vincent and Associates) placed between the flats was used to block the nonreflected radiation and created a photobleaching pulse when briefly opened. The intensity ratio of the photobleaching pulse to the probe beam was -109. Following the flats, the radiation was split by a 50:50 beam splitter BS1 into two mutually coherent beams which were crossed at the sample by means of a Mach-Zehnder interferometer. The interferometer consisted of two fixed mirrors M1 and M2 and a moveable triangular mirror MJ to allow convenient adjustment of the angle between the beams. Before intersecting at the sample, the beams were rotated (by two mirrors, Md and M5, oriented at 45" to the beam propagation and 90" relative to each other) to allow the beams to intersect in the vertical plane (Figure 1, inset). Care was taken so that the path diflerence of the beams did not exceed the coherence length (several centimeters) of the laser radiation. The beams were imaged into the TIRF flow cell and intersected and internally reflected at the solid/liquid interface with p polarization. Under these conditions, the resultinginterference pattern has a fringe spacing 4 described by eq 1, where 8, the angle of incidence, and 4, the angle the intersecting beams make with their bisector, are shown in Figure 2. The fringe spacing was changed by altering the intersection angle of the ~~
(28) Kopel, D. E. Bioflhys.J. 1979,28,281.
Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
493
Figure 2. Angle of incidence, 8,and angle of intersection, 24, for the excitation beams that experience total internal reflection at the
interface. Figure 3. Fluorescent probe molecule, rubrene, an eight-ring polycyclic aromatic hydrocarbon. Photooxidation of the probe occurs by formation of an endoperoxide product, where the bridging oxygens span one of the two central rings.30
beams through movement of the triangular mirror M3. In this way, the same interference pattern was varied for both the photobleaching and probing radiation. The TIRF cell (Figure 1, inset) consisted of a quartz dove prism with end angles of 72" in contact with the fused silica sample slide. Glycerol was used as an index-matching fluid to eliminate reflections at the prism/slide interface. Fluorescence from the slide/solution interface was collected with a camera lens L1 of f / # = 1.4, passed through a filter F1 to block the laser line and imaged onto a photomultiplier tube (Hamamatsu R928) that was terminated at 1 MS2 with a filtering 0.1 pF capacitor to reduce shot noise. The fluorescence recovery signal was digitized and stored with a digital oscilloscope (LeCroy 9410). Sample Preparation. A polished, fused silica slide was used as the planar substrate on which C-18 ligands were bound. The slide was cleaned with a hot 1:l mixture of nitric and sulfuric acid, rinsed with glassdistilled (Coming) and purised water (Barnstead, Nanopure ID, and dried in an oven at 120 "C in the cleaned reaction vessel for several hours prior to use. C-18 ligands were bound to the substrate by refluxing for 12 h with octadecyldimethylchlorosilane (Hiils) in toluene dried over 4 A molecular sieves prior to use. Approximately 200 mL of toluene was used with a greater than 5Ckfold excess of reagent. A large reagent excess was difticult to avoid due to the small surface area of the silica slide and reaction vessel. In addition, 5 mL of pyridine was added to the mixture as an acid acceptor catalyst. Following derivatization the slide was washed with anhydrous methanol and tetrahydrofuran VHF) and dried on a vacuum line. After an experiment, the slide was cleaned with THF and methanol to remove any dye and stored under anhydrous methanol. Slides stored under methanol were rinsed with water and allowed to equilibrate with the mobile phase used in the next experiment. Derivatized slides were mounted in the TIRF flow cell. A solution containing rubrene was flowed through the cell against the slide to introduce the probe into the C-18 layer. The dye solution consisted of rubrene dissolved in a tetrahydrofuran/water mixture. In order to avoid probe/probe interactions in the C-18 layer, the amount of sorbed rubrene was kept under 1.1%of a monolayer. These conditions were determined chromatographically. Chromatographic Measurements. A reversed phase chromatographic column of G18 derivatized silica particles was packed in house and used for chromatographic measurements. The effective surface area of the alkylated silica was estimated from the amount of material needed to pack the column, and the reduction in surface area of -36% when the 60 A pore diameter silica was derivatized with C-18 ligandsm The volume of the mobile phase in the column was estimated from the elution of a
the concentration of dye in solution, C, was chosen to give the desired surface concentration, C,. Considerations of capacity factor and solubility of the probe led to a mobile phase composition with a THF/water ratio of 40%/60%by volume. Dye concentrations were chosen to produce an equilibrium surface concentration of 0.3-1.1% of a monolayer. To measure surface diffusion coefficients,the dye solution was removed and replaced with a 0, 10, or 20% (by volume) methanol in aqueous solution and equilibrated for a minimum of 5 min; no changes in diffusion coefficient were observed over a 20 min period following equilibration of the surface. No dye concentration dependence on the measured diffusion coefficients was observed. Data Acquisition. With a bleaching beam intensity of 100 mW, photobleaching pulse durations were chosen such that the signal following bleaching was 290% of the prebleach signal, or the bleaching ratio was 50.1. For the sinusoidal excitation pattern used in this experiment, maximum fractional recovery occurs at small bleaching ratios.27 The bleaching ratio was chosen such that the recovery could be observed just above the background noise level. Typical pulse durations were 30-50 ms. Rubrene (Figure 3),was chosen as a fluorescent probe because of its high fluorescence quantum efficiency, strong hydrophobic character, and photoinstability. Rubrene photooxidizes easily and controllably at moderate laser intensities to an endoperoxide product having no visible abs~rption;~~ recovery of the peroxide-bridged product species at room temperature is not observed over a period of weeks. Under the conditions of the experiment, therefore, rubrene is permanently photobleached. Typically, five fluorescence recovery transients were taken at each fringe spacing; the sample was translated to an unexposed region between laser shots.
(29) Roumeliotis, P.;Unger, IC IC /. Chromatog. 1978,149, 211.
(30) Emsting, N. P.;Schmidt, R; Brauer, H.-D.]. Phys. Chem. 1990,94,5252.
494 Analytical Chemistry, Vol. 67, No. 3, February 1, 7995
norretained dead-volume marker, D ~ 0 . 2Chromatographic ~ capacity factors for rubrene were measured as a function of mobile phase composition. By altering the THF/water ratio of the mobile phase, the retention of rubrene could be controlled. An estimate of 100 & per rubrene molecule was used to estimate a maximum surface coverage. Based on the capacity factor, k', measured from the chromatographic retention time, 9 corrected for the unre tained peak time, to, and the surface area and mobile phase volume of the column, A, and V , , respectively
(3)
Data were acquired at five different fringe spacings for each solvent condition. Data Analysis. Each fluorescence transient was fit to a singleexponential recovery
F(t) = A - B exp(-t/tr)
-
,
.
,
.
,
.
I
.
+++*++
+
,
tl
.
f t
(4)
where the time constant of the recovery contains the diffusion coefficient D according to eq 2. Data were fit by a nonlinear leastsquares routine using a Marquardt alg0rih-1~~ compiled in FORTRAN. T i e constants determined from five transients at a given fringe spacing were averaged and their spread was used to estimate the variance in the results. The uncertainty of the time constants along with the uncertainty in fringe spacing itself was used in a weighted, linear least-squares fit of l / t r versus l/@. The weighted fit was completed using a linear algebra a p p r ~ a c hdescribed ~~ by the matrix equation:
K=XB+R
0.177
(5)
where K is a vector containing inverse recovery time constants,
1
i
,,
0.165 0
10
20
30
40
50
Time (sec) Figure 4. Fluorescence recovery transient due to diffusion of rubrene at a C-18 silicdwater interface. Included is a fit of the data to a single-exponentialrise with time constant rr of 9.4 s.
recovery was entirely due to diffusion within the fringes. Diffusion coefficients for each solvent condition were determined in triplicate by the above procedure and combined in a weighted average to estimate the uncertainty in the reported results.
X is a design matrix having a column of ones corresponding to the intercept and a second column containing the inverse squares of fringe spacings, 1/@,and B is a response vector containing the slope and intercept. Since the residuals, R, are not of homogeneous variance, eq 5 can be multiplied on both sides by a weighting matrix, W, that causes the weighted residuals, WR, to be drawn from a population of constant variance:
wK=wxB+wR
(6)
The maximum likelihood criterion for estimating the response vector B minimizes the sum of the squares of the weighted residuals, RWW R; this condition gives rise to a set of two normal equations, the solution to which is given by32
51 = (xw~-'(xwwQ
(7)
where primes indicate the transpose of the matrix. The weighting matrix W is created by placing the inverse of the standard deviations from elements of K on the matrix diagonal with zeros everywhere else. The matrix product of WW is, therefore, a square matrix with diagonal elements equal to the inverse of the variance for each element in the vector K Creating the W matrix from the standard deviations of the trvalues is straightforward. However, the uncertainty in the fringe spacings must also be incorporated in the W matrix. This was accomplished by an iterative process that mapped the errors from the fringe spacings onto the errors of the time constants through the slope of the fitted line.33 The iirst estimate of the slope was calculated with a W matrix containing only the errors from the time constants. The iterative process was repeated until the slope (equal to 4&D) did not change by more than one part in The intercept of the best fit of the data, corresponding to an infinite fringe spacing where 1/@= 0, was examined to test whether the fluorescence (31) Press, W. H.; Flannery, B. P.; Teukolsky, S.A;Vetterling, W. T. Numericol Recipes: Cambridge: London/New York, 1986. (32) Draper, N. R;Smith, H. Applied Regression Analysis, 2nd ed.; Wiley: New York, 1981;Chapter 2. (33) Irvin, J. A; Quickenden, T. I. 1.Chem. Educ. 1983,60,711.
RESULTS AND DISCUSSION An example fluorescence recovery transient from the diffusion of rubrene on a (2-18derivatized silica surface in contact with pure water is shown in Figure 4. The fringe spacing for the excitation beam for this experiment was 7.8 pm. Following a bleaching pulse at 488 nm of 3.5 mJ (100 mW for a 35 ms duration), the fluorescence from the sample recovers in the form of an exponential rise as rubrene molecules migrate from the unbleached regions into the illuminated regions by diffusion across the surface. Superimposed on the data is a least-squares fit to a single exponential with time constant tr= 9.4 s; the recovery data are well described by a singleexponential function over the entire five time constant duration of the experiment. Fluorescence recovery time constants determined from five different transients at a given fringe spacing were averaged, and their variation about the average was used to estimate the uncertainty in the results; typically, the relative standard deviation of tr results was -12%. The variation of the recovery rate, l h r , with the square of the inverse fringe spacing, l/@,was used to determine the surface diffusion coefficient of the rubrene probe molecule; from eq 2, one would expect a plot of l/trversus l/@to yield a straight line having a slope equal to 4n2D. Since the uncertainty in the recovery rate, l/rr, varied with the fringe spacing (see Figure 5), and the fringe spacing itself carries additional uncertainty from the measurement of beam crossing angle (see eq l),a weighted, linear least-squares fit of l/trversus l/@was carried out using an iterative process to include the uncertainty in fringe spacing, as described in the Experimental Section. The variations in recovery rate with the inverse square of the fringe spacing were in all cases linear (see Figure 5); an F-test at the 95%confidencelevel could not detect any significant deviation of the data beyond the uncertainty in the fitted straight line. In all cases, the uncertainties of the intercept included zero; a nonzero intercept would indicate either that diffusion across the entire laser spot was occurring on the time scale of the experiment, that adsorption of the probe from solution was taking place, or that the photobleaching step was reversible on the time scale of the experiment. Since the intercept was indistinguishablefrom Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
495
1.2 1.o
3 6 2
e 3
0.8
0.6 0.4
0.2
0.0
2
0
4
8
6
10
12
14
1/d; x 10' (cm") Figure 5. Determination of surface diffusion coefficient. A plot of the fluorescence recovery rate, 1hr,versus the inverse square of the fringe spacing, l/#. The straight line is the weighted linear leastsquares fit of the data; the best-fit slope is 7.60 (& 0.40)x 1O-* cm2 s-' = 4$D. Error bars on the recovery rate data indicate the 95% confidence limits. n
3
3.2
w
3.0
"0
2.8
w
3
Y
2.6 2.4
. I
0
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1
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U 1.8
.-8
a
2 a
1.6 1.4 1.2
0
2
4
6
8
10
12
14
16
18
20
% Methanol in Overlaying Solvent Figure 6. Diffusion coefficients for rubrene in a C-18 surface layer versus overlaying solvent composition. Methanol concentration in aqueous solution is percent by volume. The error bars represent the 95% confidence limits.
zero in all cases, the fluorescence recovery was entirely due to diffusion within the fringes. In order to increase the number of degrees of freedom in the fit and to remove covariance from the uncertainty of the slope arising from the intercept, the data were refit with the line forced through the origin so that the slope was the only fitting parameter. Figure 5 shows an example l/r, data versus l/# fit to a line having a slope of 7.60 (f0.40)x lo-@cm2 which is equal to 4n2D. At each solvent condition, three separate experiments were performed, each producing data equivalent to that plotted in Figure 5; weighted, h e a r least-squares fits of each of those plots produced three slopes at each experimental condition that were combined in a weighted average. Diffusion coefficients were then calculated from the combined slopes, which are plotted in Figure 6 versus solvent composition. The surface diffusion rate of rubrene in the (2-18 layer increased as the concentration of methanol in the overlaying solution was increased. Diffusion 2.1 (f0.3)x and coefficients were D = 1.5 (f0.2) x 2.8 (f0.4)x cm2s-l, for 0, 10, and 20%methanol in aqueous solution, respectively; the error bounds indicate the 95% confidence limit. The increasing rate of surface diffusion of the probe with an increase in the fraction of organic modifier in the mobile phase 496 Analytical Chemistry, Vol. 67, No. 3, February 1, 1995
is likely correlated with a change in the alkyl chain dynamics. The bound surface ligands should become more mobile as the layer swell~13,~~22 and the alkyl chains sample a larger volume. As the layer extends, rubrene diffuses through a less ordered, more mobile medium. The environmentthat rubrene experiences is still very far from "liquidlike", however; this can be implied from the measured diffusion coefficients,which are approximately 3 orders of magnitude smaller than in free solution. An organic modifier such as methanol contained in the overlaying aqueous solution causes the layer to swell for several reasons. Most importantly, the chains are more easily wetted by the overlaying solvent16 Retention of methanol at the interface lowers the driving force for the chains to reduce their surface area in the presence of water through a reduction in the interfacial tension. Contact angle measurements of alkyl ligands bound to borosilicate glass slides show that the advancing contact angle decreases with increasing methanol concentrationin the solution.% Methanol may also reduce the structuring of water, subsequently reducing the hydrophobic which increases the solubility of not only hydrophobic analytes but also the bonded alkyl chains in solution. These factors combine to reduce chain density at the interface. Since the segmental motion of alkyl chains increases with increasing distance from the surface? it is not unreasonable to question whether rubrene diffuses at a faster rate at higher methanol concentrations because it is sampling different regions of the chains. As retention of solvent components at the C-18 interface occurs, a gradient of modifier develops because water is partially expelled from the alkyl ligands; as discussed by Men and Mar~hall?~ a sorbed molecule partitions into a region of the (2-18 layer of particular polarity depending on the solute characteristics. For a dansylamide probe?3 the polarity of the probed sorption region was similar to a 10%water in methanol solution over a wide range of mobile phase compositions from 2 to 50% water in methanol. Since this amphiphilic probe had a hydrcphobic tail and more polar fluorescent head group, the observed sorption environment was thought to be dominated by the ligand/ solution interface. In similar experiments using pyrene as the fluorescence probe,12J3 a much less polar sorption environment was found; the difference in sorption environments found with these two probes likely arises from their differences in polarity, which affects the retention process. Pyrene is a hydrophobic, polycyclic aromatic hydrocarbon (€'AH) that is highly partitioned into the G18 layer. On the basis of fluorescence quenching of sorbed pyrene by a solution phase quencher (I-), the probe was shown to be slightly exposed to the overlaying aqueous solution at low methanol concentration^.'^ As the concentration of methanol in the overlaying solvent was increased, quenching from solution became undetectable as the C-18 layer swelled and protected the probe from contact with the solvent. Rubrene is similar to pyrene as they are both strongly hydrophobic PAH compounds, although rubrene is slightly larger but less planar and less rigid. Rubrene is highly partitioned at low methanol concentrations, similar to the behavior of pyrene.36 With 100% water as the mobile phase, a capacity factor for rubrene, k' > 105, is predicted from the intercept of a plot of In k' versus either percent THF or percent methanol. Due to the comparable ~
~
_
_
_
~
~
~
(34) Park, J.-M.; Kim, J. H. J. Colloid Inte?face Sci. 1994,168,103. (35) Karger, B. L.; Gmt, J. E;Hartkopf, A; Weiner, P. H. J. Chromatogr. 1976, 128, 65. (36) Cam,J. W.; Harris, J. M.Anal. Chem. 1988,60,698.
2.2 2.0
2
1.8
1.6 1.4
1.2 1.o 0.00 0.01 0.02 0.03 0.04 0.05
0.06
[Hg(CH3C02)21
0.07 0.08 0.09 0.10 0.11
(MI
Figure 7. Stern-Volmer plot for rubrene fluorescence quenched by Hg(CH&O& in methanol solution. The quenching rate constant is kq = 7.8(& 0.5)x lo* s-l M-I.
size of rubrene relative to the C-18 layer and the significant degree to which rubrene is partitioned at low methanol concentrations, the observed changes in diffusion are most likely due to changes in mobility of the chains rather than rubrene sampling the interfacial region. As a test of the hypothesis that rubrene is indeed partitioned into the C-18 layer under these experimental conditions, a quenching experiment was carried out with Hgz+ (in the form of the acetate salt), an ionic quencher that does not partition into the C-18 chains (the elution of mercuric acetate from a C-18 column by water was measured versus both DzOZ1and 1,3,5trihydr~xybenzene~~ dead-volume markers, where k' 5 0.03). If rubrene is not quenched when sorbed to the C-18layer, this would indicate that rubrene was highly partitioned in the alkyl chains. Figure 7 shows a Stem-Volmer plot for free solution quenching of rubrene by mercuric acetate in methanol. Based on the slope of the line in Figure 7, and the fluorescence lifetime of rubrene (16 ns38,39 ), the rate constant for quenching of rubrene by mecuric acetate is k, = 7.8 (f0.5) x lo8 s-l M-l. If this value is corrected for a change of solvent to water and for the geometric constraints of quenching at a surface,40the expected rate constant for surface quenching would be k , , = 2 x 108 s-l M-' if rubrene is fully accessible to encounter with quencher from solution. Quenching of rubrene sorbed at a C-Wwater interface by mercuric acetate was tested experimentally,and the observed surface rate constant kq,s = 0.2 (h0.6) x lo8 s-l M-' was indistinguishable from zero; this result indicates that rubrene is well partitioned and protected in the C-18 layer from overlaying solvent. The results of the present work can be compared with several studies of interfacial diffusion in the literature. Two investigations have addressed lateral surface diffusion of molecules adsorbed to the alkylated silica/solution interface. The Grst study measured the rate of diffusion of molecular iodine on a C-1 alkylated silica.41 Adsorbed IZ was used to quench the fluorescence of pyrene covalently bound to a silica surface. It was found that the rate of quenching was enhanced when the silica was modified with C-1 ligands; the increased rate of quenching arose from the adsorbed (37) Popl, I.; Fahnrich, J. J. Chromatogr. 1983,281,293. (38) Strickler, S. J.; Berg, R A J Chem. Phys. 1962,37, 814. (39) Harris, J. M.; Chrisman, R W.; Lytle, F. E.; Tobias, R S. Anal. Chem. 1976, 48, 1937. (40) Wong, A L.; Hunnicutt, M. L.; Harris,J. M. J. Phys. Chem. 1991,95,4489. (41) Wong, A L.;Harris, J. M. J. Phys. Chem. 1991,95,5895.
quencher, and the rate of quenching was used to determine the surface diffusion coefficient of iodine. The diffusion coefficient (corrected for two-dimensional boundary conditions42) for IZ on the C-1 surface in contact with 50:50 water/methanol was 7 (* 1) x cmz s-l. As the methanol concentration was increased (up to loo%),the diffusion coefficient also increased as the surface tension at the hydrophobic ligand/solution interface was lowered. Diffusion of adsorbed iodine on the methylated silica surface in contact with 5050 methanol/water is 25 times faster than the diffusion of rubrene in a C-lBmodZed surface in contact with a 20%methanol solution. About half of this faster diffusion could be attributed to the smaller size of iodine, and an additional 40% would derive from extrapolating the results in Figure 6 to 50% methanol. Even with these corrections, there still exists, however, nearly 1order of magnitude difference between the diffusion rate of a molecule adsorbed to a methylated silica surface and a molecule partitioned into a C-18 layer. This discrepancy is even more apparent in comparing the present results with a recent fluorescence recovery study of the diffusion of acridine orange at a C-Wwater interface.26Acridine orange is protonated and cationic at neutral pH and has been shown by fluorescence polarization measurements to reside at the C-Wwater interface rather than to partition into the ~hains.4~ Acridine orange was found to diffuse laterally at a C-Wwater interface with a diffusion coefficient D = 1.3 (fO.l) x cmz s-l. While this result is comparable (within a factor 2) to the diffusion rate of iodine at a C-l/methanol-water interface, it is 100 times faster than the diffusion of rubrene partitioned into the C-18 layer in contact with water. Although acridine orange is smaller than rubrene, the small (-30%) difference in size is not expected to cause the 100-fold difference in diffusion rates. Since the charge on the probe contines its sorption to the C-18/ water interface,43acridine orange samples only the most mobile region5of the alkyl phase, namely, the ends of the chains. Since acridine orange is not fully partitioned, its diffusion is not inhibited by the much slower chain motion in the bulk of the ligand matrix, rubrene was found to be fully partitioned and reports the mobility of molecules in the bulk of the C-18 layer. This difference in diffusional behavior is consistent with the concept discussed above that interfacialz3and partitionedl2J3polarity probes can report vastly different surface environments. Two previous attempts to acquire diffusion rates of a fully partitioned probe have been described44s45in both studies, excimer formation rates of pyrene in a C-18 layer were measured. With a 75:25 methanol/water overlaying solvent, a diffusion coefficient estimated from the excimer/monomer emission ratio was D = 2.5 x cmz s - ~ at; an ~ interface of C-Wwater with a small amount of sodium tetradecyl sulfate to wet the the excimer formation rate was measured and correspondedz6to a somewhat slower diffusion coefficient D = 9 x cm2 s-l. While faster diffusion was found in the presence of methanol, which is consistent with the trends in Figure 6, the interfacial diffusion measured by excimer formation is much faster than the results of patterned photobleaching recovery. This discrepancy is surprising since pyrene and rubrene are both partitioned into the C-18 layer and are of similar size. There are differences between the structure of pyrene, which is planar, versus rubrene, (42) Wang, H.; Harris, J. M. J. Am. Chem. SOC.1994, 116,5754. (43) Burbage, J. D.;Wirth, M. J. J Phys. Chem. 1992,96,5943. (44) Bogar, R G.; Thomas, J. C.; Callis, J. B. Anal. Chem. 1984,56,1080. (45) StAhlberg, J.; Almgren, M.; Alsins, J. Anal. Chem. 1988,60,2487.
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which is larger and has pendant phenyl groups that are out of plane. Rotational diffusion of probe molecules in longchain alkane and alcohol solvents has been shown to depend on the probe molecule diffusion of large nonpolar solutes approaches the hydrodynamic Stokes-Einstein limit, whereas small solutes diffuse faster than this limit as the molecules report their motions in local solvation environments. The smaller, more planar structure of pyrene could contribute to a faster diffusion rate; however, it is unlikely that the small structural differences in the probes could account for the 2 order of magnitude discrepancy in the diffusion rates. A more significant difference between the pyrene excimer formation experiment and FRAPP is the time scale on which the experiments are performed and the corresponding distance over which diffusion is measured. The longer (several seconds) FRAPP experiment measures transport over macroscopic (micrometer) distances, whereas the diffusion of pyrene to form excimer withii the lifetime of the monomer excited state (-100 ns) is only 20 A even if the diffusion coefficient is as large as 2 x cm2 s-l. Therefore, because of the short time scale of excimer formation kinetics, the pyrene excimer experiments probe local motions of sorbed molecules, whereas fluorescence photobleaching recovery measures diffusion over distances that are large compared to molecular dimensions. The large difference in distance scale between these experiments is a critical distinction since it has been shown that ligands bound to silica are not homogeneously distributed on the surface,@ which could lead to domains of higher and lower ligand density that iduence sorption environments. In addition, the drive to minimize surface area against an aqueous solvent mixture causes the chains to tilt into the surface plane;16,20 this effect may impose local orientational order due to chain packing creating higher density regions. Hydrophobic domains created by regions of higher chain density may be preferentially occupied by pyrene; this could lead to higher local concentrations of pyrene on the surface, making the pyrene excimer formation kinetics faster than a homogeneous surface distribution of the probe. An advantage of the FRAPP experiment is that the distance scale for diffusion is established by the optical wavelength of the excitation source and not the surface concentration of probe molecules, which may not be homogeneous. Furthermore, the longer distances over which molecules must migrate across the surface averages the effects of surface microenvironments. The discrepancy between the shorter range and longer range diffusion rates can be rationalized by hydrophobic molecules being sorbed into domains on the C-18 surface where they are locally mobile (and possibly at higher local concentration). The barrier to diffusion over longer distances could be due to slow transfer
of the solute between domains or slow motions of the domains themselves. Evidence of the latter model is presented in accounting for the long-range motion of an adsorbed probe on a C-18 a model that accounted for a slow lateral diffusion rate but a very fast in-plane rotation rate49s50of the same adsorbed probe. It is intriguing that a similar sorptiondomain model might account for differences in local versus long-range motion of molecules at a (2-18 interface both at the liquid interface and withii the chains themselves. A question remains about the effects of probe size and shape on determining lateral diffusion rates. Preliminary studies indicate that pyrene can be photobleached at optical power densities that can be produced with a krypton ion laser. A FRAPP investigation of the long-rangediffusion of pyrene at the C-lS/solution interface should address the question of probe size effects on these results. CONCLUSIONS
As the solvent in contact with a C-18 phase is altered, so is the nature of the interface. The diffusion of solutes partitioned into the C-18 layer can be used to follow changes in the surface phase. The diffusion rate of a hydrophobic, sorbed probe molecule was measured when the C-18 layer was in contact with several overlaying aqueous solutions. As the methanol concentration in the aqueous solutions increased, the diffusional rate of the probe within the alkyl chain matrix increased. Faster diffusion in the presence of methanol is attributed to an increase in chain mobility caused by retention of methanol at the alkyl phase/ solution interface. Methanol allows the C-18 layer to be more easily wet by the overlaying solutions reducing the drive for the chains to minimize their surface area. As the C-18 phase swells, the chains increased in mobility and the probe could diffuse through a less rigid environment. The much slower mobility of partitioned probes over distances much longer than molecular dimensions could be related to sorption into domains where motion of the domains or between domains is impeded. ACKNOWLEDGMENT
This research was supported in part by the National Science Foundation (Grant CHEW10319). Fellowship support (to RL.H.) was received through an NIH Biotechnologies Training Grant from the Center for Biopolymers at Interfaces at the University of Utah. Use of the chromatographic column prepared by Scott Waite, assistance in experimental design by Xiao-Rong Zhu, and helpful discussions with Mary J. Wirth are gratefully acknowledged. Received for review October 3, 1994. Accepted November 29, 1994.@ AC9409750
(46) Ben-Amok, D.; Drake, J. M. J Chem. Phy. 1988.89,1019. (47) Jiang,Y.; Blanchard, G. J. J. Phys. Chem. 1994,98,6436. (48) LochmiiUer, C. H.; Colbom, A S.; Hunnicutt, M. L.; Harris, J. M. J. Am. Chem. SOC.1984,106,4077.
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(49) Wirth, M. J.; Burbage, J. D.J Pkys. Chem. 1992,96, 9022. (50) Piasecki, D. A; Wirth, M.J. Langmuir 1994,10, 1913. @Abstractpublished in Advance ACS Abstracts, January 1, 1995.
