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Langmuir 2008, 24, 6562-6566
Single-Molecule Observations of Surfactant Diffusion at the Solution-Solid Interface Andrei Honciuc, Adam W. Harant, and Daniel K. Schwartz* Department of Chemical and Biological Engineering, UniVersity of Colorado, Boulder, Colorado 80309 ReceiVed March 8, 2008 Individual fatty acid molecules adsorbed at the interface between hexadecane and fused silica have been tracked using total internal reflection fluorescence microscopy. Two cooperative diffusive mechanisms are observed: continuous small-scale Brownian motion and occasional large “jumps.” The continuous diffusion exhibits evidence of confinement. The effective interfacial diffusion coefficients for each mechanism increase systematically with temperature; an Arrhenius analysis gives an activation barrier of ∼50 kJ/mol for “jumping” and an upper limit of ∼10 kJ/mol for confined diffusion.
Introduction The self-organization of amphiphilic molecules into nanoscale assemblies is the fundamental principle behind biological structures, surfactant phenomena, and biomimetic nanomaterials such as self-assembled monolayers (SAMs). These highly ordered assemblies cannot form in the absence of molecular mobility. A quintessential example of this mobility is the interfacial transport of an amphiphilic adsorbate molecule at the boundary between a solvent and a solid substrate. Typical hypothetical scenarios involve interfacial “diffusion” or molecules “hopping” from surface site to surface site; however, direct observations are lacking. There is indirect evidence that such mobility exists. For example, our group has calculated an approximate interfacial diffusivity of adsorbed molecules during SAM growth by modeling the nucleation and growth rates of 2D clusters measured using in situ real-time AFM.1,2 Other researchers have noted the qualitative effects of lateral surfactant diffusion with respect to the control of surface wettability (autophobicity),3 self-assembled monolayer ripening,4 and resolution limits in microcontact printing.5 Other reports suggest that adsorbed surfactants maintain some mobility even when removed from solution.6–8 Traditionally, fluorescence recovery after photobleaching (FRAP) has been used to extract diffusion coefficients within thin films9,10 where fluorophores are at a relatively high concentration. FRAP provides an ensemble average and is therefore relatively insensitive to the mechanistic details of interfacial transport. Methods such as fluorescence correlation * To whom correspondence should be addressed. E-mail:
[email protected]. Tel: 303-735-0240. Fax: 303-492-4341. (1) Doudevski, I.; Hayes, W. A.; Schwartz, D. K. Phys. ReV. Lett. 1998, 81, 4927–4930. (2) Doudevski, I.; Schwartz, D. K. J. Am. Chem. Soc. 2001, 123, 6867–6872. (3) Frank, B.; Garoff, S. Langmuir 1995, 11, 4333–4340. (4) Benitez, J. J.; Salmeron, M J. Chem. Phys. 2006, 125, 044708. (5) Delamarche, E.; Schmid, H.; Bietsch, A.; Larsen, N. B.; Rothuizen, H.; Michel, B.; Biebuyck, H. J. Phys. Chem. B 1998, 102, 3324–3334. (6) Workman, R. K.; Schmidt, A. M.; Manne, S. Langmuir 2003, 19, 3248– 3253. (7) Weiss, P. S.; Abrams, M. J.; Cygan, M. T.; Ferris, J. H.; Kamna, M. M.; Krom, K. R.; Stranick, S. J.; Youngquist, M. G. Y. Anal. Chim. Acta 1995, 307, 355–363. (8) Stranick, S. J.; Parikh, A. N.; Allara, D. L.; Weiss, P. S. J. Phys. Chem. 1994, 98, 11136–11142. (9) Heitzman, C. E.; Tu, H. L.; Braun, P. V. J. Phys. Chem. B 2004, 108, 13764–13770. (10) Lopez, A.; Dupou, L.; Altibelli, A.; Trotard, J.; Tocanne, J. F. Biophys. J. 1988, 53, 963–970.
spectroscopy,11 confocal microscopy,12 and total internal reflection fluorescence microscopy13 (TIRFM), however, are capable of detecting individual fluorophores under appropriate conditions. Single-molecule methods provide information about the entire ensemble of microstates, identifying molecular-level mechanisms and using molecules to probe their local environment.14 The key technical challenge for single-molecule tracking experiments involves the nearly total elimination of background fluorescence. In some situations, the excess fluorophores can be removed (e.g., in supported bilayers,15 biomembranes,16 and Langmuir monolayers17). However, TIRFM is particularly useful in cases where excess fluorophores are necessarily present in solution because fluorescence is excited only within 50-100 nm of the interface of interest. In this article, we present an analysis of molecular trajectories of a surfactant at the fused silica (FS)-hexadecane interface. These trajectories are not described by simple 2D Brownian motion. Rather, the molecules undergo confined Brownian motion punctuated by infrequent “jumps”.18 Thus, two distinct molecular mechanisms, with characteristic diffusion coefficients and activation barriers, govern the short- and long-time surface transport processes. The nature of the interfacial diffusion also suggests that the adsorbate molecules experience a heterogeneous environment and that trajectories can be used to probe this environment. These phenomena are directly related to the assembly and stability of nanoscale structures and devices such as molecular electronics and nanoarrays. FS was chosen because it is chemically pure, and its amorphous surface represents a suitable model system for studying the effects of subtle microscopic geometric heterogeneity. Over the macroscopic length scale probed by a diffusing molecule (>1 µm) one can expect to achieve an ergodic sampling of surface sites. It is also an important surface from the perspective of SAM formation. (11) Chen, Y.; Lagerholm, B. C.; Yang, B.; Jacobson, K. Methods 2006, 39, 147–153. (12) Nie, S. M.; Chiu, D. T.; Zare, R. N. Anal. Chem. 1995, 67, 2849–2857. (13) Wazawa, T.; Ueda, M. Microsc. Tech. 2005, 95, 77–106. (14) Xie, X. S.; Trautman, J. K. Annu. ReV. Phys. Chem. 1998, 49, 441–480. (15) Schmidt, T.; Schutz, G. J.; Baumgartner, W.; Gruber, H. J.; Schindler, H. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 2926–2929. (16) Fujiwara, T.; Ritchie, K.; Murakoshi, H.; Jacobson, K.; Kusumi, A. J. Cell Biol. 2002, 157, 1071–1081. (17) Ke, P. C.; Naumann, C. A. Langmuir 2001, 17, 3727–3733. (18) Bychuk, O. V.; Oshaughnessy, B. Phys. ReV. Lett. 1995, 74, 1795–1798.
10.1021/la8007365 CCC: $40.75 2008 American Chemical Society Published on Web 05/20/2008
Surfactant Diffusion at a Solid-Liquid Interface
Langmuir, Vol. 24, No. 13, 2008 6563 metal body of the flow cell accommodated a 19 mm coverslip (0.15 mm thick) at the bottom and a superpolished, 2-inch-diameter FS wafer (MTI Corp.) at the top of the flow cell. A Kalrez O-ring (Dupont), a chemically inert perfluoro elastomer, prevented solvent leakage from the coverslip side. The FS wafer and the glass coverslip were separated by a 0.12-mm-thick Teflon spacer (Figure 1). The thickness of the coverslip and Teflon spacer were chosen to match the working distance of the 60× (Nikon) water immersion objective (i.e., 0.27 mm). Finally, an anodized aluminum ring was screwed into the Al body on top of the cell in order to compress a 2-inch-FS wafer, Teflon spacer/gasket, coverslip, and Kalrez O-ring and make the flow cell liquid tight. The temperature was controlled to (0.1 K, with a Peltier-based heating/cooling stage (model TD60-STC20A, Instec Inc.) and a standalone temperature controller (model STC200, Instec Inc.). Substrate Preparation. FS wafers were washed with detergent (Micro 90, International Product Corp.), gently wiped with lens paper, and rinsed with 18 MΩ cm water (Millipore Milli-Q UV+). After detergent cleaning, the substrates were immersed in piranha solution for ∼1 h, followed by UV ozone cleaning for 60 min. AFM images of the FS substrates, prepared this way (Supporting Information) show random, gently undulating surfaces with an rms roughness of 1.4 nm and no obvious characteristic lateral length scale (where features were generally smaller than ∼200 nm). Data Acquisition. Metamorph 6.3 software (Molecular Imaging, Sunnyvale, CA) was used for the image acquisition, data processing, and shutter controls. The images acquired were 512 pixels × 512 pixels, and for 60× magnification, the corresponding pixel size was ∼0.28 µm2. The diffraction-limited spot size was ∼0.2 µm.
Results and Discussion
Figure 1. Schematic diagram of the prism-based TIRF microscope setup. The flow cell is represented only by the FS substrate and coverslip, ∼0.12 mm apart. The exponentially decaying evanescent wave, created at total internal reflection, selectively excites only the fl-PA adsorbed at the FS/hexadecane interface.
Materials and Methods TIRFM was used to track fluorescently labeled palmitic acid (flPA) adsorbed at the interface between fused silica (FS) and an extremely dilute solution, ∼5 × 10-12 M, of fl-PA (BODIPY-FLC16, Invitrogen) in hexadecane (Sigma-Aldrich). TIRF Microscope. The custom-built TIRFM setup consisted of three main components: (1) a Nikon inverted microscope (model Eclipse TE2000), (2) an Ar-ion LASER source (model 543-A-AO3, Melles-Griot Inc.), and (3) an electron multiplied-CCD camera (model Cascade-II:512, Photometrics Inc.), cooled at -70 °C, was used as a photon detector. The 488 nm excitation light was launched into a single-mode optical fiber (Oz Optics Ltd.) and directed toward the sample. The small critical angles of incidence, imposed by the total internal reflection condition, were obtained with a prism-based illumination setup, as shown in the schematics of Figure 1. Cargille fused silica matching liquid (n ) 1.4587) was used at the contact between the right angle prism and the FS wafer to minimize the light scattering at this interface. The sample’s exposure time was controlled with a Uniblitz shutter (model VMM-D3, Oz Optics Ltd.). The emission and excitation light entering the objective were separated with a dichroic mirror (cut-on wavelength ∼505 nm) and a green filter (band-pass ∼515-555 nm) (Figure 1). Flow Cell Assembly. The hexadecane solvent with fl-PA molecules were pumped into a flow cell that provided a sealed and contained environment for the in situ experiments. The aluminum
The raw TIRFM experimental data consisted of movies in which individual molecules appeared as bright diffraction-limited spots. No fluorescent spots were observed in control experiments with pure solvent. When fl-PA was added, fluorescent spots appeared (due to adsorption); some moved on the surface. We presume that immobile spots were either adsorbate molecules pinned at defect sites or small immobile clusters. Typically, a moving molecule could be observed for 10-60 s before desorbing or being photobleached; the 2D position coordinates (x(t), y(t)) were determined for 98 mobile molecules at a time interval of ∆t ) 2s by extracting the center of mass of the diffractionlimited spot from each video frame using the centroid method.19 The ubiquitous stationary fluorophores served as important internal controls for each trajectory, ensuring that the apparent motion of mobile molecules was not an artifact. A representative trajectory is shown in Figure 1, overlaid on a composite image for a molecule tracked for 58 s. Analogous apparent trajectories of stationary molecules were determined in the same way in order to determine the effective lateral resolution. A conservative empirical estimate of the position resolution was determined to be ∼80 nm by analyzing the apparent “motion” of stationary particles. An apparent “trajectory” of a stationary molecule is shown in Figure 2b for comparison, illustrating the effective limits of our position resolution. As illustrated in Figure 2, the majority of the molecular trajectories provide anecdotal support for the idea that molecules undergo confined Brownian motion punctuated by large jumps, or flights. Indeed, Figure 2 shows two apparent regions of confinement. Because fluorophores are indistinguishable, it is impossible to completely rule out the possibility that a molecule might be replaced, midtrajectory, by the nearby adsorption of a different molecule. However, this scenario is unlikely at the low concentrations of fluorophores used here; we calculate a probability of roughly 1 in 30 000 per frame. (19) Carter, B. C.; Shubeita, G. T.; Gross, S. P. Phys. Biol. 2005, 2, 60–72.
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Figure 3. Mean-square displacement 〈r2(t)〉 offset on the y axis for clarity. (a, a′) 19 °C, (b, b′) 25 °C, (c, c′) 30 °C, and (d) 35 °C. The continuous lines represent fits to (a′, b′, c′) an expression for confined diffusion at short times (confined regime) and (a, b, c, d) a straight line representing effective Brownian diffusion for the jumping regime at longer times. Figure 2. (a) fl-PA molecule tracked for 58 s on the FS surface; the trajectory coordinates are marked by line-connected empty circles. The composite image consists of 29 overlaid frames, each integrated over a 2 s time interval. (See the corresponding movie in Supporting Information). (b) The apparent trajectory of a stationary molecule on the same scale as in part a, illustrating the effective lateral resolution of the experiment.
A standard approach to analyzing random motion involves the squared-displacement distribution and its mean. We have analyzed these trajectories in the standard way, where in addition to each measured trajectory being considered to start at T ) 0 virtual trajectories are considered to begin at each subsequent time point. Given a particular trajectory, the squared-displacement values for the time interval ∆T, for example, were calculated to be
r2(∆T)1 ) [x(2∆T) - x(∆T)]2 + [y(2∆T) - y(∆T)]2 (1) r2(∆T)2)[x(3∆T) - x(2∆T)]2 + [y(3∆T) - y(2∆T)]2 (2) r2(∆T)3 ) [x(4∆T) - x(3∆T)]2 + [y(4∆T) - y(3∆T)]2 (3) Similar calculations were performed for time intervals of 2∆T, 3∆T, and so forth for each trajectory. In aggregate, these values represented an experimental sampling of the squareddisplacement distribution. In particular, the mean-squared displacement (MSD) for a given time interval was simply calculated as the average of all squared-displacement values for that time interval, 〈r2(t)〉. Graphs of 〈r2(t)〉 are shown in Figure 3 for four different temperatures. For comparison, a simple 2D Brownian random walk is characterized by the expression 〈r2〉 ) 4Dt, where D is the diffusion coefficient. Clearly, the data in Figure 3 cannot be described by a simple linear dependence. Intuitively, one can divide each data set into two regimes. For shorter time intervals, there is a fast rise followed by saturation; this is particularly apparent for the lower-temperature data. For longer time intervals, a linear dependence resumes. We note that this behavior is in marked contrast with control experiments on supported lipid bilayers15 in which the trajectories were consistent with a 2D (20) Gyorvary, E.; Wetzer, B.; Sleytr, U. B.; Sinner, A.; Offenhausser, A.; Knoll, W. Langmuir 1999, 15, 1337–1347.
random walk and gave a diffusion coefficient of ∼1 µm2/s, consistent with our own FRAP experiments and values reported in the literature.15,20 A deviation from conventional Brownian motion (i.e., anomalous diffusion) is often associated with structural heterogeneity and/or multiple diffusive mechanisms. A common ad hoc approach involves a generalization of the random walk to include power law behavior;18,21 the heterogeneity can also be discrete, as in the case of confinement within a compartment.22,23 In the latter case, 〈r2〉 asymptotically approaches a value related to a characteristic length-scale of the compartment.24,25 The lines drawn through the short time interval regime (Figure 3 a′, b′, c′) represent the best fits to an analytical expression24 describing Brownian diffusion within a square compartment with reflective boundaries. In all cases, the fits return a compartment size L ) 2.4 ( 0.9 µm; the effective continuous diffusion coefficients, Dcont are discussed below. For longer time intervals, 〈r2〉 goes through an inflection point and then rises approximately linearly, deviating from the confined diffusion behavior. Qualitatively, this is due to the fact that adsorbed molecules can escape from compartments. For long times (or large distances), the periods of confinement have an increasingly small effect on the diffusion kinetics, and the MSD data asymptotically approaches Brownian behavior with an effective diffusion coefficient associated with the jumps and the characteristic time between jumps. The lines drawn through the long time interval regime (Figure 3a-d) represent the best fits to the linear behavior expected for simple 2D random walks; values of Djump are determined from these fits. At the highest temperature (35 °C), there is no longer a clear separation between regimes because jumps become frequent enough that a molecule cannot explore an entire compartment prior to a jump. (21) Arinstein, A. E.; Gitterman, M. Phys. ReV. E 2005, 72, 021104. (22) Hellriegel, C.; Kirstein, J.; Brauchle, C.; Latour, V.; Pigot, T.; Olivier, R.; Lacombe, S.; Brown, R.; Guieu, V.; Payrastre, C.; Izquierdo, A.; Mocho, P. J. Phys. Chem. B 2004, 108, 14699–14709. (23) Murase, K.; Fujiwara, T.; Umemura, Y.; Suzuki, K.; Iino, R.; Yamashita, H.; Saito, M.; Murakoshi, H.; Ritchie, K.; Kusumi, A. Biophys. J. 2004, 86, 4075–4093. (24) Kusumi, A.; Sako, Y.; Yamamoto, M Biophys. J. 1993, 65, 2021–2040. (25) Ritchie, K.; Shan, X. Y.; Kondo, J.; Iwasawa, K.; Fujiwara, T.; Kusumi, A. Biophys. J. 2005, 88, 2266–2277.
Surfactant Diffusion at a Solid-Liquid Interface
Figure 4. Semilog plot of the integrated squared displacement distribution at (a) 2 s (continuous/confined regime) and (b) longer times in the jumping regime (offset for clarity; the label “0.1” refers to the 19° data). The solid lines represent fits to the expression given in the text.
Additional support for the two-mechanism interpretation comes from a statistical analysis that considers the cumulative (i.e., integrated) squared-displacement distribution for various time intervals, C(r2, t), which is defined as the probability that a diffusing molecule is found farther than a distance r from its original position after time t.22,26 Cumulative distributions are advantageous compared to raw distributions because they do not suffer from coarse graining and artifacts due to histogram binning. The C(r2, t) distribution was calculated by simply sorting the squared-displacement data, r2, in ascending order and assigning ranks to each data point; thus C(r2j) ) 1 - j/N, where j is the rank in the sorted order and N is the total number of sorted data points. The expected form of this distribution for a simple 2D random walk is given by C(r2, t) ) exp(-r2/4Dt).26 Figure 4 shows representative cumulative distributions plotted on a logarithmic axis versus r2/4t, so the slope can be related to an effective inverse diffusion coefficient. Figure 4a shows distributions from the continuous/confined regime (t ) 2s); Figure 3b shows distributions from the jumping regime (offset for clarity). It is apparent that the slopes of the distributions in the continuous/ confined regime (Figure 4a) vary only subtly with temperature, whereas the slopes of the jumping regime distributions (Figure 4b) vary systematically and significantly. Values of Dcont and Djump were determined by fitting these data to the above expression for C(r2, t). Thus, effective diffusion coefficients were determined for each regime by two independent methods. One used the variation of the mean-squared displacement versus time, and the other focused on the form of the entire distribution at individual times. The calculated diffusion coefficients are displayed as Arrhenius plots in Figure 5; both methods provide consistent results. The effective diffusion coefficient associated with continuous motion within compartments varies only slightly with temperature, in the range of 0.040-0.045 µm2/s, whereas the jumping diffusion coefficient increases 3-fold, from 0.015 to 0.045 µm2/s. The temperature dependence of the diffusion coefficients suggests that the large jumps involve an activation barrier of ∼50 kJ/mol whereas continuous diffusive hopping corresponds to an activation barrier with an upper limit of ∼10 kJ/mol. (26) Schutz, G. J.; Schindler, H.; Schmidt, T. Biophys. J. 1997, 73, 1073– 1080.
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Figure 5. Arrhenius plots for fl-PA on FS. Filled symbols represent the values obtained from fitting the 〈r2〉 vs t curves as in Figure 2, and open symbols represent the values obtained from the cumulative distributions as in Figure 3. The dashed lines are fits corresponding to activation energies of (a) Ea ) 49 ( 4 kJ/mol and (a′) 45 ( 10 kJ/mol for the jumping regime and (b) -5 ( 20 kJ/mol and (b′) 7 ( 5 kJ/mol for the continuous/confined regime.
Figure 6. Two hypothetical mechanisms for fl-PA diffusion on a heterogeneous FS substrate consisting of isolated hydroxyl patches distributed randomly on the surface: (a) a molecule jumping between hydroxyl patches with the breaking of two hydrogen bonds (high activation energy) and (b) a molecule sliding within a hydroxyl patch without complete detachment but rather involving a concerted hydrogen bond exchange mechanism between neighboring hydroxyl sites (low activation energy).
It is instructive to compare the values of the diffusion coefficients determined in these experiments (∼0.02-0.05 µm2/ s) with those reported for related systems. Diffusion coefficients for similar molecules would be ∼103 µm2/s in bulk solution;27 more to the point, values of 1-10 µm2/s are typical in dense lipid bilayers/biomembranes.16 For Langmuir monolayers, singlemolecule studies17,28 reported diffusion coefficients of 0.4-0.5 µm2/s. Thus, diffusion is considerably slower in the current experiments, even in the absence of molecular crowding, presumably because of molecular interactions with the solid substrate. However, the mobility is still significant in practical (27) White, J. R. J. Chem. Phys. 1955, 23, 2247–2251. (28) Forstner, M. B.; Kas, J.; Martin, D. Langmuir 2001, 17, 567–570.
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terms because a molecule samples macroscopic length scales of g1 µm in a typical surface residence time. Given the presence of hydroxyl groups on the FS surface and the potential for bidentate binding of the carboxylic acid on oxide surfaces,29 it is tempting to associate the ∼50 kJ/mol activation barrier for jumping with the combined energy of two hydrogen bonds;30 see Figure 6a . This would be consistent with the suggestion by Bychuk and O’Shaughnessy18 that hypothetical large surface “flights” could be the result of desorption, diffusion in the near-surface region, and readsorption. In principle, one might hope to obtain direct information about a fluorophore’s vertical position from fluorescence intensity measurements. Unfortunately, the relatively large intensity fluctuations of the single-fluorophore signal make this impractical. In contrast, the very small activation barrier associated with the continuous diffusion could indicate that at least one hydrogen bond remains intact during each small local step. This would require a continuous patch of surface hydroxyl groups, which would then function as a compartment; see Figure 6b. (29) Somasundaran, P.; 2nd ed.; Taylor & Francis: Boca Raton, 2006, pp 768-784. (30) Lomenech, C.; Bery, G.; Costa, D.; Stievano, L.; Lambert, J. F. ChemPhysChem 2005, 6, 1061–1070.
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In any case, whereas the details of patches and/or compartments are likely to be substrate-specific, the presence of two distinct diffusive mechanisms is expected to be a more general observation. Indeed, at the highest temperature observed (35 °C), jumps were frequent enough that the presence of compartments was not obvious; nevertheless, trajectories still indicated two diffusive mechanisms.
Conclusions Fatty acid molecules were observed to diffuse at the fused silica–hexadecane interface via a combination of continuous Brownian diffusion within apparent compartments and infrequent large jumps between compartments. These results demonstrate the ability of molecular trajectories to probe the mechanisms of molecular mobility as well as the local surface environment. Acknowledgment. We acknowledge financial support from U.S. National Science Foundation (award no. CHE-0349547). Supporting Information Available: Lateral force contrast image of a clean FS substrate and the corresponding height scan mode of the same 5 × 5 µm area of the FS surface. This material is available free of charge via the Internet at http://pubs.acs.org. LA8007365
