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Determination of Energy Barriers for Intermolecular Interactions by Variable Temperature Dynamic Force Spectroscopy† Salvador Zepeda,‡,§ Yin Yeh,§ and Aleksandr Noy*,‡ Department of Chemistry and Materials Science, Lawrence Livermore National Laboratory, Livermore, California 94550, and Department of Chemical Engineering and Materials Science, University of California Davis, Davis, California 95616 Received July 3, 2002. In Final Form: November 8, 2002 Intermolecular interactions in chemistry and biology are governed by complex potential energy surfaces. Despite recent advances in nanoscale interaction force measurements, determination of the potential energy barriers remains difficult. We present a simple force microscopy technique that can extract tipsample interaction potential depth and width from the pull-off force measurements. We show that determination of the thermodynamic parameters for the interaction requires measuring the pull-off force as a function of the loading rate and temperature. We apply this variable-temperature dynamic force spectroscopy technique to determine thermodynamic parameters for the interactions between a silicon nitride tip and a mica surface and for the interactions of tip and surface terminated with carboxylic acid functionalities in ethanol. For both cases, we observed that pull-off force increases logarithmically as a function of loading speed, with the rate of the increase determined by the width of the interaction potential. Analysis of the temperature dependence of the interaction forces provides estimates for the enthalpy and entropy of the interactions and reveals an important role of solvation effects in these systems.
Introduction Energy barriers encountered in intermolecular interactions determine kinetics and outcome of a multitude of key processes at biomolecular interfaces in nature and at man-made interfaces in materials processing. For example, complex energy landscapes that govern intra- and intermolecular interactions are ultimately responsible for the specificity of protein folding and accuracy of receptorligand recognition in biology1 and boundary lubrication and adhesion in tribology.2 Intermolecular interactions become especially important for nanotechnology, where adhesion emerges as a dominant force as the device length scale shrinks below a micron.3 Detailed information about the interaction potentials is critical to our efforts to understand, model, and control the processes at the nanoscale.4 For many years, researchers were content with either constructing the empirical interaction potentials or inferring them from indirect measurements.5 However, the recent emergence of ultrasensitive force detection techniques such as the surface forces apparatus,6 atomic force microscopy (AFM),7,8 and optical trapping9,10 has opened an exciting opportunity to probe these interactions directly. AFM is especially † Part of the Langmuir special issue entitled The Biomolecular Interface. * Corresponding author. ‡ Lawrence Livermore National Laboratory. § University of California Davis.
(1) Fersht, A. Enzimes: Structure and Mechanics; W. H. Freeman: New York, 1985. (2) Handbook of Micro/Nano Tribology, 1st ed.; Bhushan, B., Ed.; CRC Press: Boca Raton, FL, 1995. (3) Kendall, K. Science 1994, 263, 1720-1725. (4) Israelachvili, J. Intermolecular and Surface Forces; Academic Press: New York, 1992. (5) Lazaridis, T.; Karplus, M. Curr. Opin. Struct. Biol. 2000, 10, 139145. (6) Israelachvili, J. Acc. Chem. Res. 1987, 20, 415-421. (7) Binnig, G.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930-933. (8) Quate, C. Surf. Sci. 1994, 299/300, 980.
attractive, since it combines excellent force and distance resolution with the ability to probe local interactions.11 Chemical modification of the AFM tips with specific functional groups, chemical force microscopy (CFM), provides a general route for measuring specific interactions with sub-nanonewton force resolution and sub-angstrom distance resolution.12,13 This approach is valuable, since it allows systematic investigations of the very basic chemical interactions that contribute to the complex interactions at biological interfaces. Researchers have used AFM and CFM to investigate a variety of interactions ranging from basic van der Waals and hydrogen bonding to complex ligand-receptor interactions and interactions between complementary DNA strands.13-18 However, the interpretation of these measurements is often complicated, because correlation between the measured pull-off force and the interaction potential is not always straightforward.19 AFM uses a cantilever force transducer that undergoes mechanical instabilities when it senses potential gradients that are higher than the cantilever spring constant. These instabilities usually prevent AFM from mapping the complete interaction potential. Researchers (9) Ashkin, A.; Dziedzic, J. M.; Bjorkholm, J. E.; Chu, S. Opt. Lett. 1986, 11, 288-290. (10) Svoboda, K.; Block, S. Annu. Rev. Biophys. Biomol. Struct. 1994, 23, 247-285. (11) Clausen-Schaumann, H.; Seitz, M.; Krautbauer, R.; Gaub, H. E. Curr. Opin. Chem. Biol. 2000, 4, 524-530. (12) Frisbie, C. D.; Rozsnyai, L. F.; Noy, A.; Wrighton, M. S.; Lieber, C. M. Science 1994, 265, 2071. (13) Noy, A.; Frisbie, C. D.; Rosznyai, L. F.; Wrighton, M. S.; Lieber, C. M. J. Am. Chem. Soc. 1995, 117, 7943. (14) Lee, G. U.; Kidwell, D. A.; Colton, R. J. Langmuir 1994, 10, 354. (15) Lee, G. U.; Chrisey, L. A.; Colton, R. J. Science 1994, 266, 771773. (16) Noy, A.; Vezenov, D.; Kayyem, J.; Meade, T.; Lieber, C. Chem. Biol. 1997, 4, 519-527. (17) Noy, A.; Vezenov, D.; Lieber, C. Annu. Rev. Mater. Sci. 1997, 27, 381-421. (18) Skulason, H.; Frisbie, C. D. J. Am. Chem. Soc. 2000, 122, 97509760. (19) Unger, M. A.; O’Connor, S. D.; Baldeschwieler, J. D. J. Vac. Sci. Technol., B 1996, 14, 1302-1307.
10.1021/la026188c CCC: $25.00 © 2003 American Chemical Society Published on Web 01/16/2003
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have introduced several modifications to AFM that use probes with continuously variable spring constants to eliminate mechanical instabilities and map the complete interaction potential.20-22 Unfortunately, these modifications were technically involved and typically required custom-made probes, which ultimately prevented them from gaining wider acceptance. However, even conventional AFM pull-off measurements can probe the bottom part of the potential well and thus are potentially capable of providing important information about the force potential: the depth of the potential well and the width of the energy barrier that separates the bound state from the unbound state. Therefore, it is important to devise a strategy for extraction of these characteristics of the potential from the AFM data. Unger et al. previously described one such technique,19 but it required detailed knowledge of AFM probe shape and it ignored the dynamic nature of intermolecular bonds. In this paper, we show that the kinetic model of interaction strength23 provides an adequate framework for extraction of interaction potential parameters from AFM binding force measurements. We also show that accurate determination of the thermodynamic parameters for the interaction requires measuring of the pull-off force as a function of the loading rate and temperature. Finally, we apply this variable-temperature dynamic force spectroscopy technique to determine the thermodynamic parameters for the interactions of carboxylic acid functionalities in ethanol. Experimental Methods Materials and Chemicals. We used commercial sharpened silicon nitride AFM probes (Microlever D, ThermoMicroscopes/ Veeco, Sunnyvale, CA) and silicon (111) wafers (Silicon Sense, Nashua, NH). Probes and tips were used as received. Ethanol and 16-mercaptohexadecanoic acid were purchased from Aldrich and used as received. To modify the surfaces with well-defined chemical functionalities, we first coated the AFM probes and silicon wafers with 50 Å of Cr followed by 1000 Å of gold. The coatings were deposited by thermal evaporation at rates not exceeding ∼1.4 Å/s. We then immersed AFM probes and substrates in freshly made 10 mM solutions of the alkanethiol in ethanol for 12 h. The probes and samples were taken out of solution immediately before the experiment. Prior to mounting in the microscope fluid cell, probes and samples were rinsed with ethanol and dried under a filtered nitrogen stream. Variable-Temperature Dynamic Force Spectroscopy. We used a custom-built variable temperature AFM setup (Figure 1A) based on the Nanoscope II atomic force microscope (Digital Instruments/Veeco, Santa Barbara, CA). A detailed description of the setup is given elsewhere.24 Briefly, we machined a custom copper sample holder that incorporated a thermoelectric element (Omega Engineering, Stamford, CT). The holder design also eliminated the need for an O-ring seal. The temperature in the microscope cell was monitored by two thermocouples (immediately above and below the sample) and maintained by a PID feedback circuit (Marlow Industries, Dallas, TX). The microscope was enclosed in a custom two-layer environmental chamber cooled with cold dry nitrogen gas. Nitrogen also prevented water condensation on the microscope optical elements. This setup maintains the temperature in the microscope fluid cell to better than 0.1 °C precision over a wide range of temperatures. (20) Houston, J. E.; Michalske, T. A. Nature 1992, 356, 266-267. (21) Ashby, P. D.; Chen, L. W.; Lieber, C. M. J. Am. Chem. Soc. 2000, 122, 9467-9472. (22) Jarvis, S. P.; Yamada, H.; Yamamoto, S. L.; Tokumoto, H.; Pethica, J. B. Nature 1996, 384, 247-249. (23) Merkel, R.; Nassoy, P.; Leung, A.; Ritchie, K.; Evans, E. Nature 1999, 397, 50-53. (24) Zepeda, S.; Yeh, Y.; Orme, C. A. Rev. Sci. Instrum. 2001, 72, 4159-4163.
Figure 1. (A) Schematics of the experimental setup for our measurements. We mounted the tip and the sample in a temperature-controlled fluid cell of the atomic force microscope. A two-stage environmental cooling chamber encloses the instrument. The inset shows a cartoon of the AFM probe and sample modified with the self-assembled monolayer terminated with COOH functionalities. (B) A schematic representation of a generic tip-sample interaction potential under the influence of the external loading force. The dotted line shows the unloaded interaction potential, the dashed line shows the external loading force potential f(t) x, and the solid line shows the interaction potential tilted under the external load. Cantilever Spring Constant Calibration. Large variations in the spring constants of the commercial cantilevers require individual calibration of every cantilever used for quantitative measurements. We calibrated our cantilevers individually over the experimental range of temperatures using the thermal resonance method.25 As we reported previously, the spring constants of the gold-coated cantilevers decrease with increasing temperature.26 To account for this effect, we calibrated the spring constant for each cantilever at every temperature point in our measurements. The limited precision of the thermal resonance method (15%) is one of the main sources of uncertainty in our experiments. Adhesion Force Measurements and Data Processing. We measured adhesion forces by recording AFM cantilever deflection in the “force curve” cycle. The magnitude of the pulloff jump in the retraction part of the force curve provided the measure of the adhesion force. To measure binding force as a function of loading rate, we kept the approach rate constant at 50 nN/s and varied the retraction rate. Binding forces measured in the AFM experiments always display significant fluctuations caused by the variations in the tip-sample contact area and a bond formation probability that is less than unity. To quantify these uncertainties in our measurement, we recorded at least (25) Hutter, J. L.; Bechhoefer, J. Rev. Sci. Instrum. 1993, 64, 18681873. (26) Noy, A.; Zepeda, S.; Orme, C.; Yeh, Y.; De Yoreo, J. J. Am. Chem. Soc., in press.
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300 individual binding force measurements for every temperature point and for every loading rate value. We need to emphasize that these uncertainties do not reflect the precision of the AFM measurements but rather are a fundamental feature of the AFM measurement. To avoid introducing further systematic error in the data associated with tip wear, we varied the loading rates in random order. When we recorded binding force data as a function of temperature, we kept the loading rate constant. The uncertainty in the pull-off force measurements increased with the loading rate increase. A similar increase in the binding force uncertainty was previously observed by Merkel et al.23 In contrast, when we measured binding force as a function of temperature, the uncertainty in the measurements did not show any noticeable trend. AFM probes modified with self-assembled monolayers are often susceptible to catastrophic failure of the gold coating. Nevertheless, we were able to determine both the temperature and loading rate dependence of the adhesion force with a single modified tip, largely because we used sharp probes that yielded small values of the interaction forces. Low values of the spring constant for our tips also minimized the stress on the gold coating associated with the loading phase of the measurement. We used IgorPro data analysis software (WaveMetrics, Lake Oswego, OR) and a set of custom procedures (courtesy of Dr. D. V. Vezenov) to extract the values of the adhesion force from the force curves.
barrier and separated the energy barrier into enthalpic and entropic components, E0 ) ∆H - T∆S. Then, a simple rearrangement of eq 3 gives
fpull-off )
[ ]
kT ∆H ∆S kT Tln xβ xβ xβ rfτDxβ
(4)
Equation 3 predicts a logarithmic dependence of the binding force on the loading rate rf with the slope equal to kBT/xβ, thus providing a way to extract the value of xβ from the experimental data. Recently,26 we considered different sources contributing to the effective energy
The first two terms in eq 4 describe the enthalpic and the entropic contribution to the bond strength, and the (always negative) third term describes the “thermal weakening” of a bond caused by the thermal fluctuations helping the system to overcome the activation barrier. Significantly, if we measure the temperature dependence of the binding force and if the interaction potential width xβ has already been determined from the binding force versus loading rate experiments, we then can determine the ∆H and ∆S for the interaction. Thus, a combination of these two measurements provides comprehensive information about the interaction potential. Before we consider the applications of this model to the AFM experiments, we need to note several assumptions. In most cases, the contact area between the AFM tip and the sample involves a finite number of bonds. Our model does not consider these bonds individually; rather, it lumps their contributions into one effective tip-sample interaction potential. Furthermore, the model assumes that the energy barriers are separated along the reaction coordinate. Undoubtedly, these are significant simplifications and a model that treats the dynamics of each bond in the contact area separately will provide a better description. Yet, we found that even our simple model captures the basic physical features of the AFM pull-off experiment. We now turn to the application of this model to the analysis of the experimental data. To benchmark the kinetic model approach, we measured adhesion forces as a function of loading rate and temperature for a silicon nitride tip and mica surface (Figure 2A,B). As predicted by the model, the adhesion force increased logarithmically as a function of loading rate over 4 orders of magnitude (Figure 2A). The observed logarithmic dependence shows that at slow loading rates the binding strength is dominated by a single energy barrier.29 The slope of the dependence at low loading rates corresponds to the interaction potential width of 12 Å. Interestingly, the dependence at loading rates higher than 10-7 N/s shows a higher slope that corresponds to the interaction potential width of 1.4 Å. This phenomenon corresponds to the exposing of the tighter inner potential barriers at higher loading rates. Previously, Merkel et al. observed similar behavior for the interactions of biotin and streptavidin in the dynamic force spectroscopy experiment.23 Strunz and co-workers observed similar scaling in their measurements of unbinding of single DNA molecules.30 When we measured adhesion force as a function of temperature at loading rates that correspond to the high end of the outer barrier range, adhesion force increased with the temperature. We have already reported such counterintuitive behavior and attributed it to the entropic barrier that arises from the ordering of the solvent molecules at the interface.26 We also demonstrated that these solvationdominated barriers can be a major feature of the interactions between hydrophilic surfaces in hydrogen-bonding solvents. Our values for barrier widths compare well with the thickness of water solvation layers on the mica surface
(27) Evans, E.; Ritchie, K. Biophys. J. 1997, 72, 1541-1555. (28) Hanggi, P.; Talkner, P.; Borkovec, M. Rev. Mod. Phys. 1990, 62, 251-341.
(29) Evans, E. Faraday Discuss. 1998, 1-16. (30) Strunz, T.; Oroszlan, K.; Schafer, R.; Guntherodt, H. J. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 11277-11282.
Results and Discussion We begin by describing the behavior of a chemical bond or an ensemble of chemical bonds under an external loading force. Evans and Ritchie recently introduced a simple model that captures essential details of the system’s physical behavior.27 Their model is based on the transition state theory28 and treats the unbinding process as a kinetic problem of the escape from a potential under the influence of the external loading force. This external load tilts the interaction potential and facilitates thermally activated escape from the bound state. Evans and Ritchie describe the rate of escape from the bound state dP/dt under applied load f(t) as a first-order process:27
dP ) -koffP(t) dt
(1)
where the rate constant koff contains a term that describes the reduction of the activation barrier due to the external loading force f(t):
koff )
(
)
E0 - f(t)xβ 1 exp τD kBT
(2)
Here E0 is the activation energy barrier, xβ is the distance between the bound state and the transition state, and τD is the characteristic diffusion time of motion in the system. The solution of eq 1 for the case of constant rate loading of the bond with rate rf, which is the typical loading regime for AFM experiments, gives the following expression for the pull-off force:27
[
kBT ln fpull-off ) xβ
]
( )
τDxβ exp
kBT
E0 kBT
+
kBT ln rf xβ
(3)
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Figure 2. Binding force between the Si3N4 AFM tip and the mica surface measured in ethanol (A) as a function of loading rate at room temperature and (B) as a function of temperature. As we varied the temperature, we kept the loading rate constant at 12.6 nN/s.
measured using high-resolution specular X-ray reflectivity.31 In those experiments, Cheng et al. observed a tightly bound first solvation layer at 2.5 Å (determined from the position of oxygen atoms) followed by a loose hydration layer extending to ∼10 Å. Therefore, it is likely that in our system the tightly bound first solvation layer of the ethanol molecules gives rise to the inner barrier at 1.4 Å, and loose ethanol solvation layers cause the outer barrier at 12 Å. To compare our results for the Si3N4/mica system with the behavior of the system that presents a well-defined chemical interaction, we used our method to characterize the interaction potential for the probe tip and the surface terminated with carboxylic acid functionalities. Binding force measured in this system in ethanol also showed a logarithmic increase with the loading rate (Figure 3A). The measured slope of the dependence corresponds to a barrier width of 1.32 Å. Ashby et al. used gold-coated tip and sample surfaces modified with thiol self-assembled monolayers to show that at tip-sample distances smaller than 3 Å the interaction is dominated by surface chemical functionalities rather than van der Waals interactions between gold coatings.21 Therefore, we can rule out van der Waals interactions as a possible origin of the observed interaction. Our barrier value compares well with the reported distance of 1.72 Å between hydrogen-bonded water molecules in an ice crystal.32 However, it would be misleading to attribute this barrier to pure hydrogen (31) Cheng, L.; Fenter, P.; Nagy, K. L.; Schlegel, M. L.; Sturchio, N. C. Phys. Rev. Lett. 2001, 8715, 6103, U6186-U6188. (32) Jeffrey, G. A.; Saenger, W. Hydrogen bonding in biological structures, study ed.; Springer-Verlag: Berlin, 1994.
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Figure 3. Binding force between the COOH-terminated AFM tip and the COOH-terminated surface measured in ethanol (A) as a function of loading rate at room temperature and (B) as a function of temperature. As we varied the temperature, we kept the loading rate constant at 49.1 nN/s.
bonding, because binding force measured in this system also increased with the temperature (Figure 3B). This behavior again indicates that the entropic contribution from the solvent ordering at the interface dominates the energy barrier. The measured barrier width is very similar to the width of the inner barrier that we observed for Si3N4-mica interactions, strongly suggesting that this barrier also originates from the tightly bound ethanol solvation layer. Surprisingly, we were unable to observe evidence for the outer barrier in this system. One possibility is that the outer solvation layers at the selfassembled monolayer surface are much more disordered than the similar layers at the mica surface and thus do not contribute significantly to the solvation barrier. We combined the variable-rate and the variabletemperature binding force measurements to determine the thermodynamic parameters of the interaction potential. We can use eq 4 and the measured values of xβ to estimate the entropy and the enthalpy of unbinding from the slope and intercept of the force versus temperature dependence. Table 1 summarizes the interaction potential parameters that we obtained for our two experimental systems. Notably, for both Si3N4-mica and COOH-COOH interactions, the absolute value of the barrier entropy that we obtain for our effective tip-sample potentials is larger than the value of kB; therefore, on the time scale of our experiments the thermal fluctuations are indeed insufficient to break solvent ordering that creates both of these barriers. It is somewhat more difficult to use the intercept to estimate the enthalpic component of the energy barrier since both the enthalpic and kinetic terms in eq 4 contribute to the intercept. Thus, the enthalpy values that we obtained from the intercept can be treated only as a
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Table 1. Intermolecular Interaction Parameters Determined from Data in Figures 2 and 3a probe
sample
Si3N4
mica
Au/COOH
Au/COOH
xβ, Å 11.65 ( 3.54 1.43 ( 0.40 1.32 ( 0.36
∆H, J -1.44((1.03) ×
∆S, J/K 10-19
-1.10((0.24) × 10-19
-7.10((0.35) ×
E0, J 10-22
-4.85((0.86) × 10-22
E0, kJ/mol
10-20
40.70
3.49 × 10-20
21.03
6.78 ×
a
In the last column, the values of energies in units of kJ/mol were obtained by multiplying the energy values in the previous column by Avogadro’s number NA.
lower estimate of the enthalpy value. We can use enthalpy and entropy values to estimate the magnitude of the energy barrier at room temperature, E0, to be 3.49 × 10-20 J (21.03 kJ/mol) for COOH-COOH interactions. This value compares well to typical energies for the hydrogen bonds between acetic acid molecules of 15.7 kJ/mol.32 However, this correspondence highlights one of the advantages of direct determination of interaction energies. If we obtained our values for the energy barriers in our system using an indirect method, it would have been tempting to attribute the interaction to pure hydrogen bonding. However, our experimental data clearly show that the real interaction is much more complicated and indicate the important role that solvation and the entropic barriers play for both systems. A comparison between the measured binding force and energy values highlights another feature of the interaction potentials in our system. The measured binding force for COOH-COOH interactions is about 5 times larger than the measured binding force for Si3N4-mica interactions, yet the calculated energy value for COOH-COOH interaction is only half the energy value for Si3N4-mica interactions! Clearly, the large difference in binding forces originates from the significantly lower barrier width for the case of COOH-COOH interactions. Even if the depth of the barrier is comparable in both cases, a much narrower potential well for COOH-COOH interactions caused by a tightly bound first solvation layer leads to significantly higher unbinding forces. This comparison demonstrates that there is no straightforward correlation between a single measured binding force value and interaction potential. Finally, we want to discuss the applications of these measurements to a wider problem of determining the energy landscapes of intermolecular interactions. Our measurements show that many factors can shape these landscapes and that the solvent in particular can make an unexpectedly large contribution. Therefore, we always need to consider an energy landscape in the context of a particular solvent. Moreover, complete characterization of a particular interaction with AFM techniques at the very least must include measurements in multiple solvents. In addition, we note that AFM geometry constrains the reaction coordinate to the direction of the probe axis; therefore, these measurements provide only a slice through the potential energy surface. Further refinements in experimental techniques are necessary to address these issues. Conclusions In summary, we showed that we can use variabletemperature dynamic force spectroscopy to extract thermodynamic parameters of the interaction potentials from experimental measurements of the pull-off forces. We demonstrated this approach for two experimental systems
presenting interactions of hydrophilic surfaces in ethanol. The kinetic model of interaction strength provided the theoretical framework for our analysis. We determined the width of the interaction potential by measuring the binding force at different loading rates. We then used this value to determine the rest of the interaction potential characteristics from the binding force dependence on the temperature. The measured potential width and depth for COOH-COOH interactions compare well with previously reported values for hydrogen-bonding species. Significantly, our measurements highlight the importance of solvation barriers in the interactions in these systems and show that the interaction is dominated by the entropy of solvent ordering at the interface. Our results show that a straightforward correlation between the measured interaction forces and interaction energies is often misleading. Instead, only a careful exploration of the system parameter space will reveal the true interaction potential characteristics. Variable-temperature dynamic force spectroscopy provides an experimental approach for such exploration. We believe that our results open up significant new research possibilities for investigations of intermolecular interactions. In its current form, our approach is especially valuable for studies of forces that arise from collective behavior of molecules at interfaces such as hydrophobic interactions or structural and entropic forces, which are difficult to study by other methods. Suitable chemical modification of the AFM probes with proteins, coupled with careful chemical control of nonspecific interactions and solvent ordering, will open up the possibility to determine protein-ligand interaction potential parameters. New probes, such as chemically modified carbon nanotube AFM tips,33 offer extensive control over the tipsample contact area and the number of interacting functionalities, which should provide additional capabilities for characterization of intermolecular interactions. We believe that our technique will find its place in the modern arsenal of force microscopy methods which will collectively reveal the truthful picture of interaction potentials between chemical and biological species. Acknowledgment. S.Z. acknowledges N. Tsvetkova, R. E. Feeney, W. Fink, V. Krishnan, and D. Nguyen for helpful discussions and LLNL Student Employee Graduate Research Fellowship support. We thank C. Talley for proofreading the manuscript. This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory, under Contract No. W-7405Eng-48. LA026188C (33) Wong, S. S.; Joselevich, E.; Woolley, A. T.; Cheung, C. L.; Lieber, C. M. Nature 1998, 394, 52-55.
