Single-Molecule Probing of Mixed-Mode Adsorption at a

The remaining 1% of the molecules became specifically adsorbed during ... Molecular Approaches to Chromatography Using Single Molecule Spectroscopy. L...
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Anal. Chem. 1998, 70, 5264-5271

Single-Molecule Probing of Mixed-Mode Adsorption at a Chromatographic Interface Mary J. Wirth* and Derrick J. Swinton

Department of Chemistry & Biochemistry, University of Delaware, Newark, Delaware 19716

This paper reports the use of single-molecule spectroscopy to observe directly the presence of two disparate types of adsorption sites on a liquid chromatographic surface. This so-called mixed-mode adsorption is believed to be the physical origin of tailing of proteins and pharmaceuticals in HPLC. Single-molecule spectroscopy was used to probe the organic dye 1,1′-dioctadecyl3,3,3′,3′-tetramethylindocarbocyanine perchlorate (DiI), which was adsorbed to the interface of water and a silica surface chemically modified with dimethyloctadecylsiloxane (C18). Using low concentrations of interfacial DiI, single dye molecules were isolated by confocal microscopy, with the fluorescence from the illuminated interface monitored as a function of time. Two types of adsorption events are shown to be distinguishable by the level of fluctuations on their fluorescence signals: (1) laterally diffusing molecules having strong fluctuations on their fluorescence due to the random walk of the fluorophor about the Gaussian beam profile and (2) specifically adsorbed molecules having constant fluorescence within the shot noise. The study of 2048 single molecules entering the beam revealed that 99% of the observed molecules underwent diffusion at the water/C18 interface, and the diffusion coefficient of the ensemble was 1.3 × 10-6 cm2/s. The remaining 1% of the molecules became specifically adsorbed during observation, presumably to sites on the exposed silica substrate, and they remained specifically adsorbed for an average time of nearly 1 s. This represents the first direct experimental observation of the phenomenon that underlies tailing in chromatography. Mixed-mode retention is a long-standing problem in liquid chromatography, undermining the quality of both analytical- and preparative-scale separations of biologically important compounds, such as proteins and most pharmaceuticals. The term mixedmode means that the retention is due to the presence of at least two disparate types of adsorption sites: abundant sites associated with fast desorption kinetics and rare sites associated with slow desorption kinetics. Zone tailing occurs under this circumstance.1 For chemically modified silica gel, the chemical modifiers are believed to comprise the abundant sites and the exposed silica substrate is believed to contribute the rare sites. There is ample evidence that tailing correlates with the charge of the exposed silica, due both to the acidity of silanols and to charged sites from (1) Lenhoff, A. M. J. Chromatogr. 1987, 384, 285-299.

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metal ion contaminants.2-4 Tailing is minimized by (1) the use of highly pure silica as the substrate, (2) use of silica that is fully hydroxylated to achieve minimum acidity,5 (3) end-capping to minimize exposure of the silica substrate, (4) operation at low pH to protonate the negatively charged sites, and (5) introduction of other cations into the mobile phase to compete for the charged sites. Despite these steps, tailing continues to be a problem. A quantitative relation between surface chemical properties and the amount of tailing has not been achieved. Even qualitatively, it is not known how much of tailing is due to silanols and how much is due to impurities, thus providing little guidance for future improvements. To relate surface chemistry to tailing would require knowledge of the adsorption isotherm and the kinetics of adsorption and desorption for each type of adsorption site. To illustrate, for a bi-Langmuir adsorption isotherm, where θ is the fractional surface coverage and a is the analyte activity, one would need to know the adsorption coefficients, K1 and K2, for the two sites, and the fractional coverages, f and (1 - f), of the two sites on the surface.

aK1 aK2 θ)f + (1 - f) 1 + aK1 1 + aK2

(1)

The adsorption coefficient is the ratio of the adsorption and desorption rate constants, kads and kdes, respectively.

K ) kads/kdes

(2)

If the parameters in eqs 1 and 2 were known, the remaining data needed to describe a chromatographic zone mathematically are transport properties in the mobile phase.6 One difficulty in describing real systems with these equations is that the silica surface itself is heterogeneous, with isolated, geminal and vicinal silanols at the surface.2 Gas chromatographic studies of adsorption isotherms have shown a heterogeneous distribution of energies for adsorption to bare silica.7 Liquid chromatographic studies, where T-jump was used to probe adsorption/desorption kinetics, have shown that significant exposure of the silica (2) Cox, G. B. J. Chromatogr. 1993, 656, 353-367. (3) Nawrocki, J. Chromatographia 1991, 31, 177-192. (4) Nawrocki, J., J. Chromatogr. 1997, 779, 29-71. (5) Ko¨hler, J.; Chase, D. B.; Farlee, R. D.; Vega, A. J.; Kirkland, J. J. J. Chromatogr. 1986, 352, 275-305. (6) Felinger, A.; Guiochon, G, J. Chromatogr., A 1994, 658, 511-515. (7) Pyda, M.; Stanley, B. J.; Xie, M.; Guiochon, G. Langmuir 1994, 10, 15731579. 10.1021/ac980632s CCC: $15.00

© 1998 American Chemical Society Published on Web 10/24/1998

substrate increases the distribution of sorption rate constants.8,9 Despite the heterogeneity, it is believed that certain “strong” adsorption sites control tailing, and if these types of sites could be identified, the problem could be addressed directly. Tailing requires two circumstances: (1) the adsorption rate for one type of site is much smaller than the other, i.e., (1 - f) kads,2 , f kads,1, and (2) the desorption rate constant for this same type of site is also much smaller, kdes,2 , kdes,1. Under these circumstances, the populations of adsorbates on the two types of sites are not nearly as disparate as the adsorption rates because the rarer sites are populated disproportionately due to the slow desorption rate. Despite a great deal of indirect evidence, there has been no direct experimental evidence that the two circumstances required for tailing actually exist for chromatographic surfaces. Single-molecule spectroscopy is ideally suited to the investigation of heterogeneous chemical systems.10 Keller et al. pioneered single-molecule detection in liquids,11-12 and Zare et al. introduced confocal microscopy as a sensitive means of probing single molecules in liquids.13,14 The experiments of both of these groups laid the groundwork for the experiments reported here. Other aspects of chemical separations are being investigated by singlemolecule spectroscopy: Moerner et al. have studied single molecules in polyacrylamide gels,15 and Ramsey et al. have studied single-molecule diffusion in the mobile phase of a CE microchip.16 The purpose of this work is to evaluate single-molecule spectroscopy as a means of probing the disparate adsorption processes associated with mixed-mode retention. The mobile phase is water and the stationary phase is dimethyloctadecylsiloxane (C18) covalently bonded to silica. This is the most commonly used chromatographic stationary phase and is widely known to give tailing of organic cations. These are the first singlemolecule spectroscopic investigations of mixed-mode retention, and the system has the following simplification to facilitate interpretation: the cationic fluorescent probe is one that has a negligible solubility in the mobile phase, allowing all of the fluorescence to be attributable to adsorbed species. Desorption thus changes the fluorophor’s position on the surface rather than removing the fluorophor from the surface. 1,1′-Dioctadecyl3,3,3′,3′-tetramethylindocarbocyanine perchlorate (DiI) is a singly charged organic cation having two octadecyl chains that render it virtually insoluble in water. It adsorbs strongly to a water/ hydrocarbon interface, and its high quantum efficiency makes quantitative single-molecule studies possible, as shown previously by Betzig and Chichester,17 and Trautman and Macklin.18 The primary adsorption sites of this amphiphile are expected to be at the water/C18 interface. Numerous studies by our group of (8) Harris, J. M.; Marshall, D. B. J. Microcolumn Sep. 1997, 9, 185-191. (9) Waite, S. W.; Marshall, D. B.; Harris, J. M. Anal. Chem. 1994, 66, 2052. (10) Schutz G. J.; Schindler, H.; Schmidt, T. Biophys. J. 1997, 73, 1073-1080 (11) Soper, S. A.; Shera, E. B.; Martin, J. C.; Jett, J. H.; Hahn, J. H.; Nutter, H. L.; Keller, R. A. Anal. Chem. 1991, 63, 432-437. (12) Goodwin, P. M.; Ambrose, W. P.; Keller, R. A. Acc. Chem. Res. 1996, 29, 607-613. (13) Nie, S. M.; Chiu, D. T.; Zare, R. N. Science 1994, 266, 1018-1021. (14) Nie, S. M.; Chiu, D. T.; Zare, R. N. Anal. Chem. 1995, 67, 2849-2857. (15) Dickson, R. M.; Norris, D. J.; Tzeng, Y. L.; Moerner, W. E. Science 1996, 274, 966-969. (16) Kung, C. Y.; Barnes, M. D.; Lermer, N.; Whitten, W. B.; Ramsey, J. M. Anal. Chem. 1998, 70, 658-661. (17) Betzig, E.; Chichester, R. J. Science 1993, 262, 1422-1425. (18) Trautman, J. K.; Maklin, J. J. Chem. Phys. Lett. 1996, 205, 221-229.

Figure 1. Schematic optical diagram of the Zeiss microscope and additional optics. Each SF is a spatial filter, and APD is an avalanche photodiode.

another amphiphilic organic cation, acridine orange, showed that it undergoes lateral diffusion at the water/C18 interface;19-22 therefore, DiI is expected to behave similarly. The secondary adsorption is expected to occur at charged sites on the silica substrate, on the basis of the enormity of evidence over the last few decades of liquid chromatography. Such adsorption would be identifiable by virtue of the fact that the adsorbate would stop diffusing during its residence at these rare sites. EXPERIMENTAL SECTION Optics. An optical diagram is shown in Figure 1. A modelocked argon ion laser operated at the 514.5-nm line was used for excitation. The laser was passed through an equilateral prism and then spatially filtered (SF1). This minimized the amount of plasma glow and achieved a nearly Gaussian beam profile of controllable diameter. A Zeiss Axiovert microscope with an oil immersion objective (NA ) 1.30) was used to illuminate the interface and to collect fluorescence from the interface. The fluorescence filter set had a narrow-band excitation filter to block the remaining plasma glow, a dichroic filter to reflect 514.5 nm and transmit the fluorescence, a band-pass emission filter to isolate fluorescence, and a second cutoff filter to reduce Raman emission from water. A power of 1.7 mW was focused to a beam diameter (e-2) of 10 µm. The light at the focal plane of the TV port was spatially filtered (SF2) and then imaged onto a 100-µm pinhole (SF3) to reduce background emission beyond e-3 of the beam profile. The pinhole was mounted on an xyz translation stage having micrometers for sensitive positioning. The light passing through the pinhole was imaged onto the active area of an actively quenched avalanche photodiode (EG&G Canada). This spatial filtering typically reduced the background by a factor of 3 without affecting the size of the signal. Electronics. Time-filtering was used to reduce the large Raman background that results from the presence of the water at the interface. For time-filtering, the stop pulse for a time-toamplitude converter (Oxford-Tennelec) was generated using a fast (19) Kovaleski, J. M.; Zhu, X. R.; Harris, J. M.; Wirth, M. J. Anal. Chem. 1994, 66, 1708. (20) Kovaleski, J. M.; Wirth, M. J. J. Phys. Chem. 1995, 99, 4091. (21) Kovaleski, J. M.; Wirth, M. J. J. Phys. Chem. 1996, 100, 10304. (22) Kovaleski, J. M.; Wirth, M. J. J. Phys. Chem. 1997, 101, 5545.

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Figure 2. Photon counts vs time. Each point is acquired over a 4-ms dwell time.

photodiode to monitor the laser output, and the signal was sent into a discriminator to convert it into NIM pulses. The TTL output of the avalanche photodiode was used as the start pulse for the time-to-amplitude converter. The single-channel analyzer output of the time-to-amplitude converter was sent to a multichannel scaler (Oxford-Tennelec) to monitor counts as a function of time. A time window of 3.5 ns, beginning just after the maximum of the scattering signal, was found to reduce the background more than 7-fold relative to the signal. A 4-ms dwell time was selected for the multichannel scalar, and the data sets were 16 384 points. A Matlab program was written to analyze the large data sets. Sample. A fused-silica coverslip was mounted in a Teflon flow cell, which was bolted tightly to the microscope. The fused-silica 5266 Analytical Chemistry, Vol. 70, No. 24, December 15, 1998

cover slips were obtained from Esco products, the same source used in our previous studies of acridine orange at chemically modified silica surfaces.19-22 The cover slips were cleaned in a 50:50 mixture of water and concentrated nitric acid overnight and were derivatized with chlorodimethyloctadecylsilane by the same procedure used previously,19 which gives both fused-silica and chromatographic surfaces coverages of 3.3 µmol/m2 of C18 groups. Interference fringes from the thin cover slips precluded the use of FT-IR spectroscopy to confirm the coverage, but the advancing contact angle of water was measured to be 90°, which indicates (23) Montgomery, M. E.; Green, M. A.; Wirth, M. J. Anal. Chem. 1992, 64, 1170.

Figure 3. Same as Figure 2. A specific adsorption event is apparent beginning at 21 s.

expected coverage was achieved.23 The DiI was deposited on the surface by first exposing the surface to a low concentration of DiI in methanol, rinsing with clean methanol, and then rinsing several times with 14 mM sodium dodecyl sulfate at pH 2 until the concentration was significantly less than 1 molecule in the beam. The SDS solution was then replaced by pure, 18-MΩ water at neutral pH. The insolubility of DiI in water prevented its

desorption during the experiment. This procedure prevents crystallites from precipitating onto the surface. Visual inspection through the eyepieces of the microscope confirmed the absence of crystallites, which are easily distinguishable from single molecules: crystallites fluoresce much more brightly, their emission wavelength is shifted red, and they photolyze gradually rather than abruptly. Analytical Chemistry, Vol. 70, No. 24, December 15, 1998

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RESULTS AND DISCUSSION Figure 2 illustrates a typical signal from the single-molecule experiment, where a burst appears each time a molecule enters the beam. In Figure 2a, the scan over 65 s shows bursts of fluorescence from single molecules are detectable well above the background emission level of 13 counts/4 ms. One subset of bursts is shown on an expanded scale in Figure 2b, illustrating the large fluctuations in the count rate due to Brownian motion of the fluorophor about the Gaussian beam profile. Figure 2c shows on a more expanded scale the individual data points comprising the burst, illustrating the typical time scale of a few tenths of a second for diffusion in to and out of the beam. No evidence of specific adsorption was observed in this scan: all bursts showed substantial intensity fluctuations attributable to Brownian motion. Single molecules in this experiment can be observed through the eyepiece once the eye is dark-adapted. Visual inspection revealed that diffusing molecules are in the great majority, but occasionally a diffusing molecule stops, remains stationary for a short period of time, then continues to diffuse. Figure 3 shows a 65-s scan where an obvious specific adsorption event occurred at 21 s. Figure 3b shows on an expanded time scale that the fluorecence count rate remains constant for 3.5 s, except for one spike occurring at 24.3 s. This spike is attributed to a second molecule briefly diffusing into and then out of the beam. Except for this spike, the count rate fluctuates within the shot noise, as expected for a molecule remaining stationary. The interpretation of specific adsorption is further supported by the fact that the fluorescence remains constant for a time period significantly longer than the typical time a molecule spends in the beam, which is qualitatively apparent from Figure 3a. The specific adsorption event is preceded by diffusion of a molecule, evident on the time scale of Figure 3c. This diffusing molecule is quite likely, but not necessarily, the same molecule that subsequently adsorbed. A very large number of photons were detected from this molecule during the time it was adsorbed, 20 500 photon counts. This is sufficient for assessing such properties as lifetime, orientation, or spectrum, from which information about adsorption sites could be obtained in future experiments. Figures 2 and 3 are a synopsis of the fundamental processes that govern tailing in chromatography: abundant weak adsorption events combined with rare, strong adsorption events. To gauge the statistics of specific adsorption, 12 consecutive scans of 65 s were made. Given that the time scale of motion is what is being used to distinguish between diffusion and specific adsorption, the diffusion coefficient must be determined. The diffusion coefficient was measured by autocorrelation of five measurements of intensity vs time, obtained using a 1-ms dwell time. The autocorrelation decay, shown in Figure 4, was fit to the theoretical function G(τ).

G(τ) )

A +B 1 + τD/σ2

(3)

This is the same autocorrelation function derived for fluorescence correlation spectroscopy using a focused Gaussian beam profile of variance σ2,24 except that the depth of focus is set to infinity to (24) Elison, E. L.; Magde, D. Biopolymers 1974, 13, 1-17.

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Figure 4. Autocorrelation of photons counts vs time. The circles represent the data points, and the solid curve is the best fit to eq 3.

represent the case of fluorophors remaining in plane of the interface. A and B are constants. The beam profile was characterized using a CCD camera and was found to have a variance of 2.42 µm2. Specific adsorption was assumed to be sufficiently rare and last sufficiently longer than the 1-ms dwell time that it contributes only to B in eq 3. The diffusion coefficient calculated from the fit to the data is 1.3 × 10-6 cm2/s. This value is about 2-fold smaller than that for acridine orange at the same interface,19 which is reasonable considering the larger size of the fluorophor. The normalized probability function, F(∆r), for the radial displacement, ∆r, in a time interval, ∆t, of a diffusing molecule is described by a Gaussian in accord with Fick’s second law, with the variance proportional to the diffusion coefficient, D, in onedimension.

F(∆r) )

1 exp(-∆r2/4D∆t) x4πD∆t

(4)

Therefore, for a small number of observations, the molecule is more likely to have displacement smaller than its root-mean-square value of (2D∆t)1/2. A diffusing molecule having several successive displacements that are much smaller than (2D∆t)1/2 could be mistaken for a molecule that is specifically adsorbed. A large number of observations would uncover such statistical anomalies. The higher the shot noise and the shallower the beam profile, the more likely it is that a mistaken identification would be made. The diffusion coefficient and the beam profile can be used to establish a quantitative basis for distinguishing between diffusing and stationary molecules. We compute the probability, P, of the diffusional displacement being less than or equal to a positional change, ∆rmax, that would maintain the fluorescence within the shot noise. Given I as the number of counts per 4 ms, and 4I1/2 as the shot noise, ∆rmax depends on the slope of the beam profile, dI/dr.

∆rmax ) 4I1/2/(dI/dr)

(5)

A diffusing molecule remaining within ∆rmax would be mistaken for a stationary molecule at least half the time. However, with

Figure 5. Radial position in the beam vs m, the number of consecutive channels of constant intensity that would occur 1:2000 times due to diffusion. The solid curves represent m for various beam intensities, and the dotted curve represents m for the beam profile used in this experiment.

successive channels, m, the net probability, Pm, of displacement remaining smaller than (2Dt)1/2 eventually becomes negligible. The probability, P, of the molecule remaining within ∆rmax after time ∆t is the integral of the F(∆r) from 0 to ∆rmax, which is expressed concisely as an error function.

P ) erf

{

}

4I1/2/(dI/dr)

x2D∆t

(6)

Given N as the number of bursts, a probability of Pm ) 1/N would mean that there is one diffusing molecule, on the average, maintaining a position whose intensity lies within (2I1/2 for m consecutive measurements. To conservatively interpret a constant intensity as being due to an adsorbate, the number of consecutive points must be greater than m. By substitution of the above relations, m is known.

m ) -(log (N)/log (P))

(7)

If the number of consecutive points measured experimentally for a burst having constant intensity matches the value of m in Figure 5, the burst has equal probability of being an adsorbate or a diffusing molecule. These relations show that the value of m varies with the beam intensity, the local slope of the intensity, and the diffusion coefficient. This derivation has an oversimplication: the additional shot noise from small displacements within ∆rmax is not included. The effect of excluding this shot noise works in the direction of making the decision more conservative. A plot of m vs radial position is illustrated in Figure 5 for Gaussian beams of three different beam intensities and N ) 2000. Imax represents the counts per unit time at the center of the beam. The information in the Figure 5 summarizes the limitations in distinguishing between diffusing molecules and adsorbates. At very short radial positions, the slope approaches zero; thus the uncertainty in radial position increases sharply, requiring m > 80 to distinguish between diffusion and specific adsorption. At very

Figure 6. Experimentally determined beam profile (circles) and Gaussian of the same variance (2.42 µm2). Both are plotted vs radial position in micrometers.

long radial positions, the slope again becomes small; thus the distinction again requires m > 80. Positions between 1σ and 2σ require the fewest consecutive points for a decision. Comparison of the three curves illustrates that higher beam intensity requires fewer points to make a decision. The dotted line in Figure 5 accounts for the background noise of 13 counts/4 ms and for the actual beam profile, which is shown in Figure 6. For the actual beam profile, Imax was estimated from the highest single-molecule data points and their shot noise. Figure 5 show that the background noise reduces the useful range at short radial positions. Figure 5 also shows that the wings on the beam profile have the advantage of extending the useful range at long radial positions; consequently, no attempt was made to force the beam profile to fit better to a Gaussian. Due to the steep increase in m after 2.5 standard deviations, a threshold in the software was used so that all data points beyond this distance were neglected. The analysis presented here shows that the key to distinguishing specific adsorption from statistical variations in single-molecule diffusion is to have a narrow and intense beam, fast molecular diffusion, and slow desorption from specific sites. The specific adsorption event evident in Figure 3 at 21 s has 822 consecutive points at constant intensity at 38 counts/4 ms. Its average intensity places it at 2.4 standard deviations from the center, and Figure 5 indicates that m ) 20 at this position for the actual beam profile. The observed 822 points greatly exceed the minimum of m ) 20 points in Figure 5, thus allowing the event to be identified as specific adsorption rather than diffusion. Six other representative bursts attributed to specific adsorption are shown in Figure 7, where the dotted lines representing the (2σ levels of the shot noise are included in each panel. Panels a-c of Figure 7 are longer bursts plotted on the time scale of 2 s and panels d-f of Figure 7 are shorter bursts plotted on the time scale of 200 ms. For Figure 7a-c, the specific adsorption persists longer than the mean time between bursts, which was calculated to be 300 ms. This mean time agrees with prediction by Poisson statistics, a property of single-molecule behavior that was illustrated by Ramsey et al.16 Since the duration of adsorption in these three cases is significantly longer than the mean time between bursts, other diffusing molecules are likely to enter into the beam during adsorption. In Figure 7a, four diffusion events are observed during the specific adsorption that persists from 35.5 Analytical Chemistry, Vol. 70, No. 24, December 15, 1998

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Table 1. Summary of Specific Adsorption Events no. of data points measured fraction of data points above background no. of bursts observed no. of bursts exhibiting strong adsorption probability of strong adsorption (%) fraction of molecules only diffusing fraction of molecules strongly adsorbing

Figure 7. Six bursts attributed to specific adsorption. The dotted lines show the 95% confidence levels for the shot noise in each case: (a-c) longer bursts plotted on the 2-s time scale; (d-f) shorter bursts plots on the 200-ms time scale.

to 36.3 s. It is possible that the diffusion at the end of the adsorption time is due to the adsorbate itself diffusing further in to and then out of the beam. This cannot be distinguished from the possibility that another molecule happened to diffuse into the beam when the specific adsorption event ended. Similarly, the diffusion immediately preceding adsorption could also be due to the subsequently adsorbed molecule. In Figure 7b, there is apparently a second diffusing molecule in the beam just after the adsorption event began. In Figure 7c, the intensity remains constant for 88 consecutive points and then drops slightly and remains constant for another 29 consecutive points before disappearing. This curious behavior was only observed once, and the decrease could be due to a spectral change of the adsorbate, which was previously reported for single molecules of DiI in a poly(methyl methacrylate) film.18 Further investigation is needed. No other molecule appears to have entered the beam during the 0.8 s that this molecule remained adsorbed. For the shorter adsorption events plotted on the 200-ms time scale, the burst in Figure 7d ends in diffusion of a molecule (likely the adsorbate), which apparently proceeded toward the middle of the beam before diffusing out of the beam. In Figure 7e, the burst begins with a diffusing molecule, likely the adsorbate, becoming specifically adsorbed on its way away from the center of the beam. The adsorbate either desorbed and diffused away from the center, which is entropically favored, or it photolyzed. In Figure 7f, a trapezoidal shape is seen, where the molecule originates from outside the beam and returns in that direction, but there is a slight divot at 5.57 s. Divots dropping all the way to the baseline were occasionally observed for specifically adsorbed molecules studied on a 1-ms dwell time. These divots are 5270 Analytical Chemistry, Vol. 70, No. 24, December 15, 1998

212992 0.13 2048 18 1 0.67 0.33

probably due to the fluorophor transiently going into the triplet state, from which it cannot fluoresce. This phenomenon whereby a single molecule stops emitting, and later resumes emitting, has been termed “blinking”.18,25-27 Since we use intensity to determine whether a molecule is stationary or mobile, blinking is discussed more fully. Two observations of blinking involved fluorescent single proteins where the blinking was attributed to slow conformational changes that switch the environment of the fluorescent moiety.25,26 A study of a dye molecule interacting with DNA in solution revealed blinking on the submillisecond scale and attributed it to transient quenching of the fluorophor by guanosine.27 DiI was observed to blink occasionally on the scale of seconds when it was incorporated in a poly(methyl methacrylate) matrix.18 This could arise from conformational changes of the polymer, which would rotate the transition moment, or it could be due to a longer-lived triplet state. In the experiments reported here, blinking on the time scale of 10-100 ms would introduce positive systematic error in the diffusion coefficient, and blinking on the time scale of 100 ms10 s would introduce negative systematic error in the average adsorption time. The only blinking of DiI in we observed in our experiments was rare and occurred on the time scale of 1 ms, as stated earlier, which negligibly affect the results. Table 1 summarizes the results of the analysis of the 2048 bursts: 18 specific adsorption events were observed, representing only 1% of the molecules that entered the beam. Four short bursts were rejected as possible specific adsorption events on the basis of the statistical grounds outlined earlier. For the specific adsorption events, the average duration of adsorption was 988 ms, which corresponds to 247 consecutive data points at constant intensity. A histogram of duration times for specific adsorption is shown in Figure 8. One would expect an exponential decay, and many more data points are required to describe the decay function. Since the data points are distributed significantly over the time axis, the histogram is consistent with a long time constant for the duration of adsorption. A value of m ) 80, the maximum height plotted in Figure 5, would correspond to a duration of 0.32 s, which occurs near the beginning of the time axis in Figure 8. Therefore, the duration of specific adsorption occurs on a long time scale relative to the beam profile and the diffusion coefficient, enabling observation of specific adsorption by this experiment. If there were a separate population of specific adsorption events whose duration had a time constant on the order of 100 ms or (25) Dickson R. M.; Cubitt A. B.; Tsien R. Y.; Moerner W. E. Nature 1997, 388, 355-358. (26) Jung, G,.; Wiehler, J.; Gohde, W.; Tittel, J.; Basche, T.; Steipe, B.; Brauchle, C. Bioimaging 1998, 6, 54-61. (27) Sauer M.; Drexhage K. H.; Lieberwirth U.; Muller R.; Nord S.; Zander C. Chem. Phys. Lett. 1998, 284, 153-163.

Relating these numbers back to eqs 1 and 2, the two circumstances required for tailing thus exist for this chemical system: (1) (1 - f)kads,2/fkads,1 ) 1%/99% ) 0.01, and (2) kdes,1/kdes,2 ) 67 × 1%/(33 × 99%) ) 0.02. For this chemical system, adsorption and desorption occur between sites on the surface rather between the surface and solution, but the activation barriers that control these kinetic parameters would also contribute to the surfacesolution rate constants. The behavior observed for DiI in this work is thus the hallmark of the mixed-mode retention responsible for tailing: rare adsorption events that inordinately populate the surface through slow desorption.

Figure 8. Histogram of the duration times of specific adsorption events.

less, this population would be missed by the present experiment. A smaller beam diameter could readily be used to explore such a possibility. Table 1 also shows that, despite the 1% probability of specific adsorption, the total time that these molecules remained adsorbed is disproportionately long. Specific adsorption is responsible for fluorescence 33% of the time that the signal is above background, while diffusing molecules are responsible for remaining fluorescence above background. Because a time average is equivalent to an ensemble-average, these percentages represent the populations of the two types of adsorbed molecules on the surface.

CONCLUSIONS Single-molecule spectroscopy is uniquely capable of isolating chemical events to enable study of heterogeneous chemical systems. By evaluating the motion of individual adsorbates, specific adsorption is identified in the presence of a 100-fold excess of weakly adsorbed molecules. This ratio of weakly bound to strongly bound adsorbates is consistent with tailing in chromatography. The automation of the instrument and data analysis pave the way for larger data sets to explore the distribution of desorption times from the strong adsorption sites and to investigate heterogeneity. A significant number of photons is emitted by the fluorophors during adsorption, potentially enabling study of adsorbate orientation and fluorescence lifetime during specific adsorption. Single-molecule spectroscopy shows significant promise as a new method for investigating the nature of the strong adsorption sites on silica that lead to tailing in chromatography. ACKNOWLEDGMENT This work was supported by the National Science Foundation under Grant CHE-9610446 and the Petroleum Research Foundation. Received for review June 9, 1998. Accepted September 21, 1998. AC980632S

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