J. Phys. Chem. B 2006, 110, 19507-19514
19507
The Origin of Surface Stress Induced by Adsorption of Iodine on Gold Drew R. Evans and Vincent S. J. Craig* Department of Applied Mathematics, RSPhysSE, Australian National UniVersity, Canberra 0200 A.C.T., Australia ReceiVed: May 25, 2006; In Final Form: July 19, 2006
The cantilever technique for the measurement of film stress on both macroscopic and microscopic cantilevers is validated, then applied to the experimental determination of film stress induced by the adsorption of a monolayer of iodine onto a gold substrate. A model is proposed that relates the change in the interatom potential upon chemisorption of iodine onto gold to the measured film stress. Excellent agreement is found with the experimentally determined value. This result gives insight into the origins of film stress that is observed in all thin film and coating applications.
1. Introduction The evaluation of surface stress is important in the application of coatings and in the manufacture of nanodevices and is also of interest for the evaluation of fundamental properties of films. Cantilever beams are employed widely for the measurement of surface stress, both in macroscopic systems1-4 and in microscopic systems.5-8 In sensor technologies, surface stress can be used to follow the adsorption of molecules,5,6,8,9-11 temperature changes,12,13 and changes in surface charge.14-17 In macroscopic measurements, surface stress is used as an indicator of a coating’s toughness,18-21 as films with excessive surface stress will easily crack or delaminate. Surface stress is also monitored in manufacturing processes to ensure that it does not result in unwanted warping of the substrate material.22-24 The measurement of surface stress using cantilever beams is not well established, and important questions as to the validity of the technique remain. In the early part of this paper, we address issues relating to the measurement and modeling of surface stress before proceeding to the evaluation of a surface stress induced by the adsorption of iodine to a gold substrate. Specifically, in Section 2, we describe the predicted profiles of cantilevers under different models of film stress. In Section 3, the profile of a macroscopic cantilever is measured to determine if the Stoney model (end moment) or Zhang model correctly describes the action of film stress. We then use microscopic cantilevers to determine that they can be used for the accurate determination of film stress if the laser spot position is known. Surface stress can be expressed as film stress, whose units are equivalent to that of film pressure, and therefore, analogies may be drawn between the film stress at the surface of a solid and the film pressure at the surface of a liquid commonly used in measurements of Langmuir-Blodgett (L-B) films. Just as the surface pressure is related to the molecular interactions between adsorbed species in L-B films, here we relate the surface stress to the molecular interactions of iodine atoms adsorbed to a gold substrate and find excellent agreement between our model and the experimental data. 1.1. Modeling and Measuring Surface Stress. The currently accepted model for the profile of a cantilever under a surface * To whom correspondence
[email protected].
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addressed.
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stress was reported by Jaccodine and Schlegel25 and is based on work presented by Stoney.26 In Stoney’s report, the profile of a plate under an applied surface stress along one of its faces was observed to have uniform curvature and, therefore, can be modeled as an end moment. Stoney derived an equation to relate the surface stress to the curvature of the surface. Jaccodine and Schlegel25 modified Stoney’s equation to account for the isotropic behavior of the surface stress when a cantilever is employed. In this version, Young’s modulus was corrected by Poisson’s ratio to give
σ)
Et2 6R(1 - ν)tc
(1)
where σ is the applied surface stress (N‚m-2), E is the Young’s modulus of the cantilever (N‚m-2), t is the thickness of the cantilever (m), R is the radius of curvature of the cantilever (m), tc is the thickness of the applied coating that gives rise to the surface stress (m), and ν is the Poisson’s ratio of the cantilever material. Across the literature, there are examples of σ being used to represent values with units of (N‚m-1)5,27-29 and (N‚m-2).1,26,30,31 This variation in units can lead to misinterpretation of experimental results. Previously, we introduced a new term, φ, to account for this unit variation, which we define as the film stress with units of N‚m-1. φ and σ are related by32
φ ) σtc
(2)
where tc is the thickness of the applied coating (m), and σ is the surface stress (N‚m-2). The film stress is related to the properties of the coating, whether it be an applied film, adsorbed molecules, or internal tension between two or more rigidly bonded materials. Film stress can also be expressed in units of J‚m-2, reflecting its origin in the energetics of lateral interactions. From herein, the film stress will be referred to but can be related back to the surface stress using eq 2. Film stress measurements with a cantilever can be used to monitor the adsorption of molecules to a substrate if the adsorption is more favorable on one side of the substrate. In this mode of operation, the cantilever is biased to allow the preferential adsorption of a target molecule by coating one side.
10.1021/jp063232e CCC: $33.50 © 2006 American Chemical Society Published on Web 09/06/2006
19508 J. Phys. Chem. B, Vol. 110, No. 39, 2006 To date, the model proposed by Stoney has been widely accepted as correct. However, an evaluation of the literature reveals that the model of Stoney has never been explicitly validated experimentally, and in recent years, alternative theoretical models for the beam shape induced by film stress have been proposed27 and a number of studies have experimentally investigated the profile of a cantilever beam that is being acted on by a film stress and varied results have been obtained. Pulskamp et al.33 measured deflections using an optical microscopy method whereby the depth of focus was used to determine the end deflection of a set of microfabricated cantilevers of different length. As the cantilevers were manufactured under nearly identical conditions, it was assumed that the magnitude of the film stress was constant from one cantilever to the next. Deflections were generally large, and therefore, comparison was made with both linear and nonlinear beam profile theories. The data were consistent with the nonlinear treatment in most cases, but in some instances, significant disagreement was observed between the experiment and both theoretical approaches. Jeon and Thundat28 used multiple light sources to measure the profile of microcantilevers due to applied film stresses. They observed nonuniform curvature that is not predicted by any theory, and also bending of the substrate to which the cantilever is attached. Miyatani et al.29 applied a film stress by utilizing the electrocapillarity of the gold coating on one face of the cantilever. When an electrode potential is applied to the system, the cantilever bends due to the stress induced along the gold surface. Accurate conclusions could not be drawn from their experiments given the small number of data points measured along the cantilever’s length. Also, the deflection measurement position could not be determined precisely given that the measurement spot size was on the order of the dimensions of the cantilever. We have previously addressed the problems associated with the determination of the illumination position on the cantilever.32 Here, we endeavor to resolve these outstanding issues. Here, we first address which model of film stress is appropriate by comparing experimentally measured beam profiles for cantilevers to the theoretical predictions for both macroscopic and microscopic cantilevers. Then once we have established the correct loading model, we will employ our previously published method32 for the evaluation of film stress to quantify the stress produced by the adsorption of iodine to a gold substrate. Further, we directly relate the observed film stress to the atomic interactions within the adsorbed layer. 2. Surface Stress Models An alternate description of a cantilever shape under an applied film stress to the model of Stoney was proposed by Zhang et al.27 The loading scenarios proposed by Stoney and by Zhang et al. are shown in Figure 1. The bending of the beam within the Stoney model is described by the application of a moment to the free end of the cantilever. The loading scenario of Zhang et al. uses a uniformly distributed stressor applied to one of the faces of the cantilever to model the uniform surface stress. A stressor is a stress tensor, having both a magnitude and a direction. Depending on the defined direction of the stressor, the stressor can model both compressive and tensile stresses. It was proposed by Zhang et al. that the stressor model would be more accurate than the other models presented. In Figure 1, the end load model is also presented for comparison. The dimensionless beam deflection and dimensionless beam curvature for three loading scenarios are compared in Figure 2.
Evans and Craig
Figure 1. Schematics of the applied moment model (A), the model proposed by Zhang et al.27 (B), and the end load model (C). Schematics (A) and (B) are proposed models for film stress. In schematic A, M represents the applied moment (Nm). In schematic B, sw represents the uniformly distributed force component and m represents the uniformly distributed moment acting at each point along the cantilevers length. P and M are the reaction force and moment, respectively. The end load is represented in schematic C by F.
It is evident that the applied moment model is different from the end load and stressor models. Surprisingly, we find excellent agreement between the end load model and stressor model. The variation between these two models are on the order of the errors expected for the numerical simulations conducted by Zhang et al. Thus we conclude that Zhang et al.’s model is equivalent to that of an end load. Why do these apparently different models result in an equivalent cantilever beam profile? The simple end load results in a linear variation in curvature along the beam. The stressor model evidently results in the same linear variation in curvature. This occurs as the summation of the many moments at points along the cantilever, each of which individually gives a constant curvature, results in a constantly varying curvature. The calculation of the cantilever beam profile for an applied end load is simpler, as it is defined by an analytical expression, whereas the approach of Zhang et al. requires a numerical solution. Comparing these models alone does not determine which is the best description for the profile of a cantilever under an applied film stress. Hence, we compare the end load, representing the approach of Zhang et al., and end moment (Stoney model) to experimental measurements of the profile of a cantilever under an applied film stress, for both macroscopic and microscopic cantilevers, to determine if they accurately describe the action of film stress. This enables the determination of the film stress due to the adsorption of iodine on gold to be made with confidence. 3. Materials and Methods 3.1. Profile of a Macroscopic Cantilever. A bimetallic strip (Scientrific Australia) made of a copper strip, approximately 150 µm thick, rigidly bonded to a 1 mm steel strip, was used as a macroscopic cantilever. The cantilever was 12 mm wide and was clamped 49 mm from its free end with two strong rare earth magnets. A 275 W heat lamp was used to uniformly heat the cantilevers. The different thermal expansion rates for the copper and steel caused the cantilever to bend. This differential expansion is equivalent to a film stress applied along one face of the cantilever. The macroscopic cantilever profile was measured using an AltiSurf 500 optical profilometer (Cotec, France). The optical
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Figure 2. Comparison of the dimensionless beam deflection and dimensionless beam curvature for the three models described in Figure 1; an applied moment (dashed), an end load (crosses), and Zhang et al.’s stressor model (dotted). It can be seen that the end load model and Zhang et al.’s stressor model are identical.
profilometer reflects tightly focused white light off the surface of interest. For tightly focused white light, the different wavelengths making up the light will have different focal lengths. By observing the wavelength of the light reflected off the cantilever, it is possible to measure the absolute distance from the light source. This is transformed into relative distances, and the profile of the cantilever is measured. The resolution of the optical profilometer used was approximately 30 nm for deflections (z) and 1 µm in the scanned direction (x). One-dimensional scans were taken along the length of the cantilever. A single scan was obtained in 6 s. For each scan, the temperature of the cantilever was measured using a Raytek MiniTemp optical temperature sensor with a resolution of 0.5 °C. The cantilever was initially heated to 30 °C and the profile measured. The cantilever was then left to slowly cool back to ambient temperature (27 °C). During the cooling process, the profile was measured at 1 min intervals and the cantilever temperature recorded. This provided a family of curves for the deflection of the cantilever at different temperatures. The measured profiles of the cantilever were adjusted for the background shape of the cantilever by subtracting the cantilever profile at ambient temperature. This enabled changes in the profile due to film stress to be evaluated without contributions to the deflection from other sources such as residual stress in the cantilever, or deflection under its own weight. Also, the optical profilometry technique described was used to determine the deflection due to an end load, from which the spring constant of the cantilever was determined to be approximately 3.0 N‚m-1. 3.2. Profile of a Microscopic Cantilever. As previous studies28,29,33 of the deflection and shape of microscopic cantilevers are not in agreement, either with each other or with measurements of macroscopic cantilevers, it is also important to examine the profile of a microscopic cantilever. A bimetallic cantilever (µMasch CSC17 AFM cantilever) made of silicon, approximately 2 µm thick, coated with a thin film of aluminum, was used. The cantilever was 50 µm wide and 460 µm long. The spring constant, k, of the cantilever was determined to be 0.3 N‚m-1 by using the thermal vibration method.34 The cantilever deflection was measured using an Asylum Research MFP-3D atomic force microscope (AFM). This AFM employs the optical lever technique to measure the deflections at a resolution of 0.4 nm. The temperature of the air surrounding the cantilever was measured using a K-type thermocouple and a K-type thermocouple preamp (ADAD595CQ thermocouple preamp chip, Analogue Devices), which was integrated with the MFP-3D acquisition hardware. The cantilever was cleaned
in an RF plasma cleaner (30 W for 30 s), then mounted in the MFP-3D air cell. A piece of glassy carbon (Sigradur G HTW GmbH) was used as the solid substrate on which the compliance was measured for calibration of the optical lever technique. The cantilever was then separated from the substrate by approximately 13 µm and left to equilibrate to the ambient temperature of 25 °C (over approximately 45 min). The deflection was then measured over a period of 45 min, where the heating was turned on after 1 min by passing a current of 600 mA through the glassy carbon, causing it to heat up and thereby heating the cantilever. The different thermal expansion rates for the silicon and aluminum caused the cantilever to bend and is equivalent to a film stress applied along one face of the cantilever. This technique is used to measure the deflection at a single point along the cantilever, and therefore, repeat measurements at different measurement positions were made. The measurement position was determined by viewing the cantilever from above via a CCD camera and the laser spot position analyzed. The cantilever was then left to slowly cool back to ambient temperature. A family of curves for the deflection of the cantilever due to an increase in temperature at different measurement positions was obtained. 3.3. Film Stress Induced by Adsorption of Iodine to Gold. A bimetallic cantilever (µMasch CSG10 AFM cantilever) made of silicon, approximately 1 µm thick, coated with a 50 nm film of gold, was used. The cantilever was 35 µm wide and 250 µm long. The cantilever deflection was measured using an Asylum Research MFP-3D AFM at a resolution of 0.4 nm. The cantilever was cleaned in an RF plasma cleaner (30 W for 30 s) then mounted in the MFP-3D fluid cell in the open configuration (not rigidly sealed) and left to equilibrate to the ambient temperature of 24 °C (over approximately 15 min). A small crystal of iodine was placed in a glass syringe and left to sublime. After approximately 120 s, the iodine vapor was injected into the cell and left to adsorb at 24 °C. The deflection was then measured over a period of 80 min. The location of the laser spot on the cantilever was determined by viewing the cantilever from above via a CCD camera. Two different cantilevers were used here with spring constants of 0.13 and 0.20 N‚m-1, respectively, determined using the Sader method.35 4. Results 4.1. Profile of a Macroscopic Cantilever. The experimentally determined macroscopic cantilever profile is compared to the two models in Figure 3. The end moment model is widely
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Evans and Craig
Figure 3. Measured deflection of a bimetallic strip under uniform film stress (solid), compared to the theoretical fits for two loading models: an applied moment (A, dots) and an end load (B, dashed). The angle of the cantilever for the experimental data and that predicted by each model is compared in C. The experimental angle was determined by differentiating the polynomial fit to the deflection vs beam span curve.
using any one of these three equations,32
φ)-
kL δappa(a - 2)2 wt(1 - ν) L
(3)
φ)-
app 2 1 δL Et a(a - 2)2 4 L2(1 - ν)
(4)
a(a - 2) 1 φ ) - δapp 4 L (1 - ν) Figure 4. Experimental data and theoretical fits of a bimetallic strip under uniform surface stress upon heating. The model of an applied moment at the free end of the cantilever is in excellent agreement with the experimental data obtained at four different temperatures.
accepted in the literature as being applicable. The end load model is equivalent to that of Zhang et al., which has been proposed as an alternative.27 The angle of the cantilever was determined by fitting the experimentally measured deflection with a sixth-order polynomial and then differentiating. Figure 3A displays the fit of the applied moment model to the experimental data, and the fit from the end load model is given in Figure 3B. The applied moment model is in excellent agreement, while the end load model poorly fits the experimental data. The excellent fit of the applied moment model is more apparent when comparing the angle of the cantilever (Figure 3C). As a further test of the end moment model proposed by Stoney, the experimentally measured profile at a range of film stress values has been compared to an end moment in Figure 4. These results were obtained at different temperatures for the bimetallic strip under uniform heating. The reported temperatures correspond to the temperature of the cantilever at the completion of the profilometer scan. The curves represent the bending due to an increase in temperature above ambient of approximately 3, 2, 1, and 0.5 °C, respectively. 4.2. Profile of a Microscopic Cantilever. A cantilever beam will deflect due to an applied film stress. When a microscopic cantilever is employed, the magnitude of the deflection is typically small, in the 10-100 nm range. To accurately measure the deflection, the optical lever technique is commonly employed whereby a laser is reflected off the cantilever onto a detector. The movement of the laser spot at the detector is typically 200 times greater than the deflection at the tip. It is necessary to calibrate the sensitivity of the optical lever (compliance), which is usually achieved by moving the tip a known distance (effectively an end load) and monitoring the voltage change at the detector. The deflections measured from the optical lever technique can be related to the magnitude of the film stress
xE(4kw)
2 3
2
(5)
where φ is the film stress (N‚m-1), k is the spring constant of the cantilever (N‚m-1), E is the Young’s modulus of the cantilever (N‚m-2), L, w, and t are the length, width, and thickness of the cantilever, respectively (m), ν is the Poisson’s ratio of the cantilever material, and a is the normalized measurement position.32 The normalized measurement position describes the position of the laser on the cantilever, which is used to determine the deflection of the beam in the optical lever technique. It is the distance at which the laser is located along the length of the cantilever from the base divided by the overall length of the cantilever (hence 0 e a e 1). In the same fashion used for the macroscopic experiments described above, film stress was induced in the microscopic bimetallic cantilever by increasing its temperature a fixed amount. Measuring the deflection allowed the magnitude of the film stress to be determined. The approximate temperature of the cantilever determined from the thermocouple as a function of time is given in Figure 5. The different lines correspond to experiments where the measurement position had been varied. The deflection of the cantilever is observed to be proportional to the temperature of the cantilever (Figure 5B). Initially, the rate of heating of the cantilever is large but decreases as the temperature of the cantilever equilibrates with the surrounding medium (after t ) 1000 s), in this case, air. There is strong correlation between the deflection of the cantilever and the increase in temperature, indicating that the heating effect is the dominant contributor to the deflection. A clear example of this is in the data obtained at a ) 0.57 (triangles). There is a large spike in the temperature at t ) 900 s, while still observing a constant slope in the deflection versus temperature plot. The deflection measured from the optical lever technique and the normalized measurement position a are substituted into eq 3 to determine the film stress induced in the bimetallic cantilever as it is heated. We note that, before heating is commenced, a film stress is present, but here we are interested in the change in stress as the cantilever is heated. The measured change in film stress is shown in Figure 6 as a function of the relative increase in temperature (∆T). On the relative scale, the film
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J. Phys. Chem. B, Vol. 110, No. 39, 2006 19511
Figure 5. (A) Temperature of a bimetallic cantilever as a function of time, measured with varying measurement positions along the cantilevers length. (B) The corresponding deflection vs temperature. The measurement positions used were a ) 0.89 (circles), 0.74 (squares), 0.66 (triangles), 0.57 (crosses), and 0.49 (diamonds).
Figure 6. Measured film stress as a function of temperature increase at several values of a. The symbols represent the measurement positions described in Figure 5.
Figure 7. Measured film stress as a function of temperature increase in water, at several values of a. The measurement positions used were a ) 0.80 (circle), 0.66 (square), 0.52 (triangle), 0.40 (plus), and 0.32 (diamond).
stress curves collapse onto one curve, illustrating excellent agreement. From this, we can conclude that irrespective of the value of a, the same stress is calculated. This experiment can also be conducted in liquid, in this case, we employed water. The cantilever used in this set of experiments had a spring constant that was determined to also be 0.3 N‚m-1 (thermal method34). The measured change in film stress as a function of temperature for several different measurement positions are given in Figure 7. Similar to the data obtained from measurements in air, the stress measured in water at a given temperature was constant irrespective of the measure-
Figure 8. Measured compliance at different measurement positions, normalized to the theoretical curve (solid line). The theoretical curve only gives the relative change in the compliance, and hence the measured compliance must be normalized (at a ) 0.736 to a relative compliance of 0.93). The theoretical curve is described by the sensitivity of the angle (eq 6). The measured compliance is in agreement with the theoretical curve when a < 0.9. The solid circles represent the values of a where the deflection due to heating of the bimetallic cantilever was measured.
ment position, with the exception of the measurement at a ) 0.32. We attribute this to a small error in the measurement of a. Before conducting any of these experiments, it is important to calibrate the optical lever technique. This is commonly done by applying an end load to the cantilever to displace the cantilever a known distance at its free end. The calibration factor is referred to as the “compliance” and typically measured in V‚m-1. The change in compliance as a function of measurement position can be described by the ratio of the angle at a to that at the free end of the cantilever (termed the sensitivity of the angle). Previously, we defined the sensitivity of the angle as,32
θa ) Sp ) -a(a - 2) θL
(6)
where θa is the angle of the cantilever at the measurement position, θL is the angle at the free end of the cantilever, and Sp is the sensitivity of the angle for an end load. The normalized compliance as a function of measurement position a is given in Figure 8. The theoretical curve (solid) gives the relative change in compliance and not an absolute measure of the compliance. The measured compliance must then be normalized to the theoretical curve at a given measurement position (in this case, normalized at a ) 0.736 to 0.93) to allow for comparison.
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Figure 9. Schematic of the cantilever highlighting the limitations of where the laser spot can be reflected. The position is limited by the location of the tip and the point at which the laser spills over the end of the cantilever. For correct measurement of the film stress, the measurement position must lie within these limits.
Evans and Craig indicating the formation of a complete iodine monolayer on the gold surface in a hexagonal close-packed (hcp) arrangement.36 We assume that adsorption of iodine to the silica face is negligible. The monolayer creates an equilibrium film stress of -0.75 ( 0.08 N‚m-1. The adsorption causes the cantilever to deflect away from the gold surface, giving the film stress a negative sign. The observation of a film stress indicates that, upon adsorption to the gold substrate, I2 dissociates and the gold surface becomes curved in order to accommodate the increase in the iodine-iodine atom spacing. The film stress measured for the two cantilevers are in good agreement. The adsorption was modeled with a Langmuir adsorption profile and found to be in agreement. Therefore, we conclude that a monolayer of iodine has adsorbed. 5. Discussion
Figure 10. Measured film stress as a function of time for iodine vapor adsorbing to a gold surface (open symbols). The adsorption is reproducible for two different cantilevers and can be modeled with a Langmuir adsorption isotherms. The solid line represents a simple Langmuir isotherm for chemisorption (dθ/dt ∝ (1 - θ)), and the dashed line represents a Langmuir isotherm for chemisorption with dissociation (dθ/dt ∝ (1 - θ)2), where θ is the total surface coverage of the iodine. For this system, the adsorption time constant, κ-1, from the Langmuir profile was determined to be approximately 900 s.
For 0.12 < a < 0.89, the compliance follows the theoretical curve. However, at values of a greater than 0.9, the measured compliance deviates from the theory. In this region, the cantilever is not taking on the shape of a cantilever under an applied end load, and hence deflections here cannot be related to φ in the manner described by eqs 3-5. The deviation from the theoretical trend represents the point at which the laser spot has moved past the loading position of the cantilever (the location of the tip). This is illustrated in Figure 9. To ensure that the deflections measured by the optical lever technique are correct, it is important to experimentally establish the value of a below which the sensitivity does not deviate from the theory. In the case presented here for this experiment, a should be less than 0.9 for reliable measurements to be made. 4.3. Film Stress Induced by Iodine Adsorption to Gold. The deflection of a microscopic cantilever with a gold face on one side and a silica face on the other was measured at a ) 0.75 for the adsorption of iodine and is shown in Figure 10 as a function of time t. The experimental data has been fit with the standard Langmuir adsorption isotherm, where the rate of adsorption is proportional to the number of vacant sites, and with a Langmuir adsorption isotherm for adsorption with dissociation, where the rate of adsorption is proportional to the square of the number of vacant sites. We find the former provides an excellent fit to the experimental data and the latter does not. This indicates that the iodine molecule only dissociates after chemisorption and immobilization of the iodine atoms on the substrate. Thus an adsorption site accommodates both atoms from a single iodine molecule. The injection of iodine vapor occurred at t ) 100 s, resulting in an immediate change in deflection. After approximately 5000 s, the film stress stabilizes,
5.1. Macroscopic Cantilever. It is clear from the experimental fits that the change in temperature of the cantilever induced a change in the magnitude of the deflection, but not the form of the profile of the cantilever. This equates to changes in the magnitude of the applied film stress. There is very good agreement between all the experimental data and the model for an applied moment at the free end of the cantilever, the Stoney model. The stressor model of Zhang et al. does not agree with the measured beam profile. However, it must be noted that, at small values of the dimensionless beam span, the agreement with the end moment model is not as good. This has been explained by Sader37 and is attributed to the isotropic nature of the film stress. The fits to the experimental data yield a film stress of approximately 2290, 1370, 588, and 407 N‚m-1 for 30, 29, 28, and 27.5 °C, respectively. Note the radius of curvature of the cantilever profile was used here to determine the film stress (eq 126). If a deflection-based technique, such as the Optical Lever technique,38 is used to determine the film stress, Stoney’s form of the equation dealing with deflection rather than the radius of curvature is in error and alternative equations should be used (see ref 32). 5.2. Microscopic Cantilever. The experiments using microscopic cantilevers in air and water are in agreement. The film stresses induced in the cantilevers are equal. This is expected, as the properties of these cantilevers are very similar (silicon and aluminum thickness, length, width, etc.) and they were sourced from the same batch. The agreement between the data is demonstrated in Figure 11, where the hollow symbols are the data collected in water and the filled symbols represent the data collected in air. These results validate the measurement technique and theoretical description employed to determine the film stress in the iodine-gold system. 5.3. Iodine Adsorption to a Gold Surface. Previous studies have followed the film stress induced by adsorption of iodine from an iodide salt solution onto the gold surface of a cantilever.16,39 Many factors, such as pH and the redox state, influence the magnitude of the induced film stress. Additionally, cations may adsorb to the silica side of the cantilever, for example, sodium ions on quartz,16 and thereby influence the measured film stress. The resulting film stress in this case is the difference between two adsorption processes, with a stress due to both the iodine on gold and sodium ions on silica. To ensure that the film stress measured is solely due to iodine, we have measured the adsorption of iodine vapor onto gold. The iodine adsorption to the silica surface (other side of the cantilever from the gold) is assumed here to be minimal.
Surface Stress Induced by Adsorption of Iodine on Gold
Figure 11. Measured film stress as a function of temperature increase in both water and air for different cantilevers. The same rate of change in stress per degree increase is determined irrespective of which cantilever is used. This indicates that the properties of the cantilevers are very similar (silicon and aluminum thickness, length, and width). Note that the number of points for the data collected in water has been reduced for clarity. Measurement positions varied between 0.32 e a e 0.89.
Figure 12. Schematic of the adsorption process of iodine to gold from the vapor phase. The iodine initially physisorbs to the surface, and upon adsorption dissociates to give iodine atoms packed in a hexagonal array, which is chemisorbed to the surface. The interatomic spacing of the adsorbed iodine (d2 ) 4.3 Å)36 is larger than the bond length of molecular iodine in the vapor phase (d1 ) 1.33 Å),40 hence, once the iodine chemisorbs and dissociates on the surface, the surface will want to expand to increase the interatomic spacing. The darkened iodine atom illustrates how each atom interacts (arrows) with its six nearest neighbors in the plane of the adsorption layer.
5.3.1. Film Stress Model. The adsorption of iodine onto a gold surface is thought to result in dissociative chemisorption. In this process, molecular iodine (I2) is physisorbed to gold. Upon adsorption, the iodine dissociates to form iodine atoms (I) that are chemically bonded to the gold and interact locally by van der Waal’s interactions. The adsorption of iodine to gold is widely accepted to create a monolayer of iodine atoms on the gold surface.36 This process is depicted in the schematic in Figure 12. Here, we attempt to relate the measured film stress to the intermolecular forces acting within the monolayer of iodine atoms. Film stress measured here (-0.75 ( 0.08 N‚m-1) can be thought of as a two-dimensional surface pressure analogous to many Langmuir-Blodgett film41-44 and chronocoulometry experiments.16 The film stress compares well with the reported values for iodine adsorbed from solution onto a Au(111) electrode (0.1-3.0 N‚m-1). Similarly, the film stress measured here is on the order of the surface pressures measured in Langmuir-Blodgett film experiments (0.01-0.6 N‚m-1). From this, we can conclude that measurements of the surface pressure and film stress probe similar properties of a monolayer, which should relate to the in-plane molecular interactions within the film.
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Figure 13. Lennard-Jones potential for interacting iodine atoms at a given separation, described by PLJ ) 4[(r/r)12 - 2(r/r)6], where is the depth of the minimum and r is the position of the minimum. The minimum is equal to the bond enthalpy of I2 (151 kJ‚mol-1) and occurs at a separation equal to the bond length in the I2 molecule (1.33 Å). The depth of the minimum gives the upper limit to the interaction energy determined from the measured film stress of adsorption.
We propose that the origin of the film stress in this system is due to the difference in the intermolecular potential between pairs of iodine atoms, originating as I2, as their interatomic distances increase during dissociation. For this to manifest as a film stress, the atoms must be chemically bound to the gold surface. At equilibrium, the area occupied by a single iodine atom is on average 14.5 Å2, which corresponds to an interatomic spacing of 4.3 Å. This spacing was obtained from LEEDS studies conducted by Ocko et al.36 for iodine electrodeposited from solution onto a Au(111) surface. In the experiments presented here, the nature of the gold is unknown, and hence, the interatomic spacing has been estimated to be approximately equal to that obtained by Ocko et al. The interatomic spacing equates to an average coverage of 6.3 × 1018 atoms per m2 (1.0 × 10-5 moles of atoms per m2), assuming that they are close packed in a hexagonal arrangement (91% surface coverage of the total available area). The Lennard-Jones potential between two iodine atoms can be used to estimate the change in potential energy associated with the change in interatomic spacing from that in the gaseous phase (1.33 Å) to that in the monolayer (4.3 Å) (Figure 13). The potential between the atoms at a separation corresponding to the bond length of 1.33 Å40 in I2 is described by the bond enthalpy of the molecule, which in this case is 151 kJ‚mol-1.40 Upon adsorption, and subsequent dissociation, the separation increases to 4.3 Å, where the potential decreases to 0.3 kJ‚mol-1. In this final state, however, each iodine atom will interact with its six nearest neighbors (hcp arrangement), and hence, the total potential in this state will be six times larger than that observed for one iodine-iodine interaction. The change in potential for iodine upon dissociation is therefore [151 (0.3 × 6)] ) 149.2 kJ‚mol-1. The value obtained here represents the upper limit that the interaction energy determined from the film stress can be. This value would be reduced by accounting for the effects from the interaction of the iodine monolayer with the underlying gold surface or the interaction of the iodine with multiple neighbors. A prediction of the total measurable film stress can be made from the change in LJ potential. The interaction between atoms occurs between pairs of iodine atoms, defined by the configuration of the original molecule before adsorption (I2). Therefore, multiplying the change in potential by half the moles of atoms per m2 (equal to moles of atom pairs per m2) yields a predicted
19514 J. Phys. Chem. B, Vol. 110, No. 39, 2006 film stress due to the interatomic forces of 0.78 N‚m-1. There is good agreement between the measured value of film stress of 0.75 ( 0.08 N‚m-1 and this predicted value from the change in LJ potential. The potential for the final interatomic spacing is small relative to the initial state; therefore, the bond enthalpy of the adsorbing molecule multiplied by the number of molecules adsorbed in a dissociative chemisorption process gives a good approximation to the measurable film stress for the adsorption. On a more general level, these results indicate that, while the measurement of film stress with a cantilever can be used in a range of sensor applications, it can also give information on a more fundamental level about the energetics that play on adsorbed materials. Specifically, it can give a measure of the atom-atom interaction energy, or in the case of particulate films, the interparticle interaction energies. Therefore, the film stress induced in any coating should be related to the change in the energy of interaction between components of the coating (atoms, particles, grains) in the plane of the film that occurs during film formation. 6. Conclusion Quantitative measurements of the surface and film stress for a range of different films and coatings can be determined from a simple measurement of the deflection of the cantilever to which the film is applied. We have established experimentally using macroscopic and microscopic cantilevers that a film stress is accurately described by an end moment as first proposed by Stoney and that the stressor model of Zhang et al., which is equivalent to an end load, is not suitable for describing film stress. Utilizing this knowledge, the stress induced upon the dissociative chemisorption of iodine to gold has been measured. This macroscopic observable quantity has been directly related to the change in interatom potential upon chemisorption to gold. This observation provides insight into the mechanisms that gives rise to the manifestation of film stress in a thin film or coating. Acknowledgment. We thank Dr. Robert Cain from Protiveris for useful discussion and comment. Also, thanks must go to Karen Hands and John Ward of CSIRO Forestry and Forest Products group for their assistance with the profilometry experiments. The helpful discussions with Yin Zhang, who willingly supplied simulation data, are appreciated. We thank the CRC SmartPrint and the Australian Research Council for support. References and Notes (1) Payne, J. A.; Francis, L. F.; McCormick, A. V. J. Appl. Polym. Sci. 1997, 66, 1267-1277. (2) Payne, J. A.; McCormick, A. V.; Francis, L. F. ReV. Sci. Instrum. 1997, 68, 4564-4568. (3) Payne, J. A.; McCormick, A. V.; Francis, L. F. J. Appl. Polym. Sci. 1999, 73, 553-561. (4) Francis, L. F.; McCormick, A. V.; Vaessen, D. M.; Payne, J. A. J. Mater. Sci. 2002, 37, 4897-4911. (5) Butt, H. J. J. Colloid Interface Sci. 1996, 180, 251-260.
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