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Application of Static Disorder Approach to Friction Force Microscopy of Catalyst Nanoparticles to Estimate Corrugation Energy Amplitudes Liron Agmon,†,§ Itai Shahar,†,§ Bat-El Birodker,† Simona Skuratovsky,† Jürgen Jopp,‡ and Ronen Berkovich*,†,‡ J. Phys. Chem. C Downloaded from pubs.acs.org by SWINBURNE UNIV OF TECHNOLOGY on 02/03/19. For personal use only.
†
Department of Chemical Engineering and ‡The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel S Supporting Information *
ABSTRACT: Friction force microscopy (FFM) of materials with well-defined crystalline surfaces is interpreted within the framework of the Prandtl−Tomlinson (PT) model. This model portrays the interaction with a surface through a deterministic periodic potential. While considering materials with polycrystalline or amorphous surfaces, the interpretation becomes more complex, since such surfaces may lack distinct lattice constant and/or corrugation energy amplitude. Here, we utilize an approach to describe the nanofriction measured on a catalyst with an irregular surface by describing the slip forces in terms of static disorder (SD) in the corrugation potential. We performed FFM measurements of the Fe−Al−O spinel catalyst powder, which is involved in reverse water−gasshift reaction. The FFM measurements resulted in intermittent stick−slip pattern with large variance in the slip forces and their spatial distribution. We compare our results with a mean version of the PT model. The two models showed close proximity of the surface energy values and their trend with the applied normal load, where the SD model estimations were less scattered. The approach presented in this work may provide a useful tool to interpret the FFM measurements of materials with irregular surfaces.
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nanocrystals aggregates.22 The Fe−Al−O spinel is a crystalline multioxide matrix designed as a novel bifunctional catalyst for the production of liquid hydrocarbon fuels and chemicals by the hydrogenation of CO2.23,24 Although the spinel catalyst possesses well-defined crystallographic planes, the recorded friction traces over its nanoparticles exhibited a wide distribution of maximal slip forces and of the distances between slip events. Corrugation energies can be calculated from FFM measurements within the framework of the Prandtl−Tomlinson (PT) model,25,26 which assumes a periodic interaction potential, making it ideal for the description and interpretation of the FFM recordings of ordered crystalline surfaces.13,14,27−30 Although highly useful and insightful, the PT model in its standard form may be considered as impractical for materials that do not possess well-defined crystalline faces, such as oxide surfaces,31−35 graphene oxide,36 amorphous carbon and diamond-like carbon films,37−39 etc. Facing this dilemma, different approaches were proposed, e.g., based on the local
INTRODUCTION Catalyst reagents are involved in a chemical reaction by binding reactant molecules to their surface, thus weakening their internal bonds. Through a sequence of various configurational changes that the reactant molecules undergo, the catalysts can direct the reaction path in a more selective route toward the desired product, which also reduces the amount of required chemical work.1 This resulted in increasing effort in studying surface phenomena and characteristics associated with catalytic performance,2−4 particularly with surface energy as a key feature for understanding the activity of inorganic catalysts.5−7 Here, we propose the use of friction force microscopy (FFM) to estimate surface corrugation energy as a useful characterization technique mainly since it is associated with adhesion energy,8 which was shown to be related to catalytic performance.5,9 FFM enables probing interactions in the single asperity level. In such a measurement, using atomic force microscopy (AFM), a sharp cantilever tip scans the surface of a substrate under application of some normal load while recording lateral (friction) forces with exceptional resolution.10−21 With the use of AFM, we performed FFM measurements on Fe−Al−O spinel catalyst, which is provided as powder comprised of © XXXX American Chemical Society
Received: December 16, 2018 Revised: January 12, 2019 Published: January 18, 2019 A
DOI: 10.1021/acs.jpcc.8b12085 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
Figure 1. Imaging and FFM measurements of Fe−Al−O spinel catalyst. (a) Topographic view (250 × 250 nm2) of the surface of the catalyst powder (top panel). The line (blue) marks a scan line whose profile is shown in the lower panel. (b) FFM images taken on the embedded catalyst powder in ethanol, in two resolutions, 500 × 500 and 250 × 250 nm2 (top and lower panels, respectively), taken as part of the identification of flat region. (c) Lateral friction force map, measured on a flat region of the spinel sample immersed in ethanol (5 × 5 nm2) measured under a normal load of 12.9 nN (top panel). Friction loop (lower panel) corresponding to the red line in the friction map above shows an erratic stick−slip pattern.
contact area33 and extending the thermally activated PT model to include the amorphous nature of the contact (PTTA model).35 Here, we implement a different approach, which is based on the static disorder (SD) in the measured parameters to interpret the recorded erratic FFM data obtained from the irregular surface of the catalyst nanoparticles. With this approach, we estimate the corrugation energy amplitude of the catalysts and found it to be comparable to the mean mechanical work and consequently with the values provided by the PT model when scaled by a factor of 2π.
300 stick−slip cycles (loops) were carried out for each scanning velocity. AFM Imaging. An Asylum Cypher-ES AFM in the AC operating mode using a sharp silicon cantilever (Olympus AC240TS) was used to image the spinel catalyst. The catalyst powder was embedded within a matrix of araldite resin (Araldite 502, Electron Microscopy Sciences) and microtomed to get a thin smooth surface. Using Tempfix adhesive, the samples were attached on top of metal coverslips.
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RESULTS AND DISCUSSION
The FFM measurements were performed in ethanol that provides a surrounding that does not interact with the catalyst. The ethanol fills the gaps between the catalyst nanoparticles as a result of physical adsorption and is not chemisorbed. Being a metal oxide, the spinel at temperatures higher than 200−300 °C may catalyze ethanol dehydration to water and ethylene or to induce condensation to higher hydrocarbons. However, all measurements were conducted at room temperature, which prevents the reaction of ethanol with the spinel catalyst. Working with a powder presents several challenges such as embedding and immobilizing the substrate and identifying flat regions of the surface to carry out the FFM measurements. Topographic AFM surface image of nanoparticles comprising the powder of Fe−Al−O material is shown in Figure 1a. This image illustrates the particle size distribution, in which the nanoparticle size varies from 15−25 up to ∼90 nm aggregates. The blue line marks a cross section over several catalyst particles. FFM imaging was performed on the catalyst sample to identify favorable 5−20 nm flat regions on the top part of the nanoparticles. Figure 1b shows two FFM images with decreasing scan size that enabled he identification of adequate scanning regions for the measurement of friction maps and
METHODS AND MATERIALS FFM Measurements. The Fe−Al−O spinel catalyst was kindly provided by the Blechner Center at Ben-Gurion University of the Negev23 as a powder (see the Supporting Information (SI) Appendix 1). The powder is composed of 3− 4 nm nanocrystals of the catalyst fused into nonporous 15−90 nm aggregates.22 A thin layer of the catalyst powder was embedded onto a thermoplastic Tempfix adhesive (Ted Pella, 16030-TN) that was homogeneously spread on a 15 mm metal coverslip (Ted Pella, GTP-16218) and then submersed in ethanol 99.9% (romical). The FFM measurements were carried out with Asylum Research Cypher-ES AFM (Oxford Instruments) at room temperature. All measurements were operated in contact mode while applying minimal integral gain. Bruker SNL-D silicon-nitride cantilevers with Si tips were used (with a nominal normal spring constant KN ∼ 0.06 N/m). Friction measurements were conducted by scanning back and forth perpendicular to the cantilever axis in various velocities ranging from 10 to 100 nm/s. Lateral calibration of the cantilever was performed using the wedge method,40−42 which returned a conversion factor of α = 150 ± 30 nN/V. At least B
DOI: 10.1021/acs.jpcc.8b12085 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
We calculated the probability distribution functions (pdfs) of the slip lateral forces, FL, and the distances between slip events, Δx, as a function of the applied normal loads, FN. The normal loads, and the number of data points used to construct the pdfs, n, were 3.6 (n = 571), 6.9 (n = 416), 10.4 (n = 366), 12.9 (n = 627), 14.7 (n = 525), 16.5 (n = 174), and 20.6 nN (n = 223). At higher loads, we could not observe any stick−slip behavior. Figure 3a plots the maximal slip forces, FLmax, the peak value of FL just before a slip occurs, against their corresponding Δx. The correlation between FLmax and Δx was estimated by calculating the coefficient of determination (see the SI Appendix 2) for each data set at the applied normal load (Figure 3a, inset). A mean value of ⟨r2⟩ = 0.098 ± 0.067 indicates a weak correlation between the lateral slip forces and the distances between them. The lack of correlation stresses the random nature of the friction recordings, as there is no particular relation with certain slip forces with specific periodicities. This behavior sets the basis for the use of the disordered approach. Figure 3b shows that although there is some small variation in the mean value of the distances between slip events, ⟨Δx⟩, its values are scattered, particularly under low loads. At normal loads higher than ∼10 nN, the distributions of Δx became narrower, although still displaying similar mean values around 0.47 nm with a relatively wide variance. Interestingly, the Δx values were consistently fitted with log-normal distributions, which can allude to the presence of more than one population of distances between slip events. Since the spinel has a welldefined crystalline structure, one would expect to observe a constant characteristic lattice parameter. However, as evident from Figures 1c and 2, the catalyst powder measured here did not display a uniform surface, unlike purely crystalline surfaces that show periodic FFM images.13,16,18,21 Since the catalyst is composed of 3−4 nm spinel nanocrystals accrued to form the powder nanoparticles,22 the uncertainty in the measured interaction with the surface is a manifestation of crossing different crystallographic planes with several oxidation levels of the iron ions23 and possibly crossing grain boundaries combined. Figure 3c shows the mean lateral slip force, ⟨FL⟩, as a function of the normal load. An increase in the mean and variance of the lateral slip forces with the applied normal load is clearly observed. The application of higher loads increases the number of interacting atoms across the tip−surface contact area, thus increasing the friction forces. However, the widening of the force distributions can be attributed to the roughness, size, and geometry of the contact region, and to the chemical interactions within it.43−46 Such a stochastic stick−slip behavior was recently reported for oxide surfaces33 and attributed to the amorphous nature of their surfaces and to reshaping of the effective contact area. The PT model used to interpret FFM measurements on crystalline surfaces describes the tip−sample dynamic interaction as a mass point sliding over a one-dimensional periodic potential. The effective interaction potential Ueff(x, t) = Uint(x) + Uel(x, t) is composed of two contributors. The first is the interaction potential of the atomic surface with the cantilever tip
loops. Figure 1c shows a lateral force map of the Fe−Al−O spinel catalyst in ethanol that was measured over the flatter, top regions of a nanoparticle, comprising repeated intermittent stick−slip patterns. FFM measurements were conducted over a range of normal loads that varied from 3.6 to 20.4 nN and scanning velocities of 0.5−5.0 s−1. Three exemplary friction loops, measured under normal loads of 3.6 pN (Figure 2a), 12.9 nN (Figure 2b), and
Figure 2. Friction loops acquired on spinel catalyst in ethanol under normal loads of (a) FN = 3.6 nN, (b) 12.9 nN, and (c) 20.6 nN. The lateral forces increase together with the dissipation (i.e., the area enclosed by the friction loop) as the applied normal load increases.
20.4 nN (Figure 2c), show an irregular stick−slip pattern. The friction measurements displayed none to mild force strengthening with the scanning velocity (see the SI), but showed a strong dependency on the applied normal load. As can be seen in Figure 2, under the application of higher loads, the measured lateral friction forces increase together with the hysteresis between the forward and backward scans. This increase of the area confined by two friction scan lines qualitatively reflects that the energy dissipation increases with normal load.15 However, the irregular nature of the stick−slip pattern, and the absence of a distinct lattice constant, is characteristic of all the traces measured at the surface of the spinel catalyst.
i 2πxt yz zz Uint(xt ) = −U0cosjjj (1) k a { where U0 is the corrugation energy amplitude, x is the timedependent position of the tip, and a is the lattice periodicity.
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DOI: 10.1021/acs.jpcc.8b12085 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 3. Lateral friction forces and position variation distributions at different normal loads. (a) Maximal lateral slip forces vs their corresponding recorded distances between slip events, Δx. The inset shows the calculated coefficient of determination for {FLmax} and {Δx} at each load. (b) Mean values of Δx with their probability densities as a function of the applied normal load. (c) Mean lateral slip force values with their probability densities as a function of the applied normal load.
The second term accounts for the position- and timedependent elastic deformation of the cantilever, Uel(x, t) = (Keff/2)(x − XS)2, where Keff is the effective lateral spring constant10,12 and XS = Vt is the position of the support of the cantilever with a scanning velocity V. The PT model may seem to be unsuitable to interpret our FFM measurements, as it assumes a periodic interaction potential. Although this serves as a reasonable approximation for ordered crystalline surfaces with a well-defined lattice coefficient, i.e., Δx = a, this is not the case for our measurements. Measuring amorphous oxide surfaces, Craciun et al. faced a similar dilemma, which they resolved by proposing an approach that utilizes a modified LennardJones potential to account for the local stick phase interaction potential instead of the periodic one in the PT framework.33 Although elegant, and highly insightful, the latter model requires the knowledge of the contact area and the tip−sample equilibrium distance, two parameters that are difficult to access. For this reason, we preferred to remain within the framework of the PT model; however, we generalize it to include static disorder in the corrugation amplitude and distance between slip events. This generalization can account for the diversity in the interaction with the spinel surfaces, as recorded in our friction trajectories. This approach was introduced by Zwanzig, who described a stochastic process of barrier crossing in terms of a disordered rate-governed process.47,48 For a deterministic barrier, (first order) reaction rate theory predicts an exponential dependency of the crossing rate. However, for a statically disordered process, described by an ensemble of barriers, the pathways explored by the measured trajectories will display a nonexponential dependency. Based on this view, Kuo et al. introduced an approximation to this approach and successfully implemented it to describe statically disordered unfolding in proteins.49 Here, we follow their methodology by considering the corrugation energy amplitude U0 and the distance between slip events Δx to be disordered parameters that can be expressed by
U0(t ) = ⟨U0⟩ + δU0(t ) Δx(t ) = ⟨Δx⟩ + δ Δx(t )
(2)
where ⟨U0⟩ is the average of the corrugation energy amplitudes, with the temporal fluctuation δU0(t), representing the disorder intensity. Similarly, the amount of disorder in Δx is given by its decomposition into its averaged value ⟨Δx⟩ and the fluctuating deviations around it δΔx(t). The interaction potential will now be given by [⟨U0⟩ + δU0(t)]cos[2πx/(⟨Δx⟩ + δΔx(t))], which is illustrated in Figure 4a, based on the force and position distributions measured at FN = 3.6 nN.
Figure 4. Static disorder description of the stochastic friction stick− slip measurements of the catalyst powder. (a) One-dimensional illustration of the statically disordered effective surface potential. (b) Calculated cumulative distribution functions (cdfs) (light blue curves), describing the mean survival probabilities of the maximal lateral slip forces at the various normal loads, fitted with the SD model (black lines) given by eq 3. D
DOI: 10.1021/acs.jpcc.8b12085 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C Implementing the SD concept into the master rate equation for crossing an energy barrier, an expression for the survival probability, S(FL), averaged over the fluctuation, i.e. the mean probability for not “slipping”, can be devised48,49 (see the SI Appendix 3) ÄÅ 2 É −1/2 l ÅÅ σ + F 2σ 2 ÑÑÑ | o o L Δx Ñ ÅÅ U0 o o (−⟨f0 ⟩FL)o ÑÑF o ⟨S(FL)⟩ = 1 − e 1 + ⟨f0 ⟩ÅÅÅ m Ñ L} 2 o Ñ o o ÅÅ (kBT ) ÑÑ o o ÅÇ ÑÖ o n ~ (3)
where ⟨f 0⟩ = [f 0/(Keff·V)]exp(−[(⟨U0⟩ − FL⟨Δx⟩)/kBT]) is the rate of crossing the mean barrier with units of [1/nN], f 0 is the attempt frequency, σU0 and σΔx are the standard deviations of the fluctuations in U0 and Δx, respectively, kB is the Boltzmann constant, and T is the absolute temperature. Note that when the fluctuations are minor, eq 3 regains an exponential dependency, which means that U0 = ⟨U0⟩, and Δx = ⟨Δx⟩. The probabilities of crossing the barrier, p(FL) (shown in Figure 3c), are related to the survival probability S(FL) = ∫ p(F)dF between 0 and FL. This means that eq 3 can be used to fit the cumulative distribution functions (cdfs) calculated for the measured slip forces at each normal load. Figure 4b shows the fittings of eq 3 (black lines) to the cdfs (light blue) at every applied load, where V, ⟨Δx⟩, and σΔx were taken from the experimental data while setting kBT = 1. From the measured traces, Keff was taken as the mean slope of the stick phase at each normal load, i.e., Keff = ⟨dFL/dx⟩. The fittings returned f 0 that vary between 0.1 and 14.9 Hz, with no particular trend with the applied load. The SD model reasonably fits the experimental cdfs, although some deviations can be observed, which may result from some of the approximations made in the derivation of the final form of the model (eq 3). One of the main assumptions in the approximated form of the SD model is that the fluctuations around the mean of the disordered parameters are normally distributed. The log-normal distribution of Δx may be the cause for the observed deviations in some of the fits. Nevertheless, the values of the mean corrugation energies obtained by this fit agreed with the mean mechanical work, ⟨W⟩ = ⟨FLmax⟩·⟨Δx⟩ (see the SI Appendix 4). We compared these values with predictions made by the PT model, according to which the mean corrugation amplitude can be calculated via15 ⟨U0⟩PT (FN) = ⟨FLmax ⟩|FN
Figure 5. Corrugation energy amplitude estimated by the SD model (light blue squares) and the PT model (purple triangles) at each applied normal load. The dashed lines are nonlinear fits intended to guide the eye.
by the PT model is about twice the value obtained by the SD model, both are two orders of magnitude higher than that of the NaCl (see the SI Appendix 5). Reflected through its surface potential, this indicates the activity of the catalyst surface compared to NaCl, which is an inert material. It should be noted that since our data did not display a plateau of the mean slip forces within the range of the applied scanning velocities, we were prevented from implementing the PTTA model35 (see the SI Appendix 6). Although the PTTA model relies on a different approach than the one presented by the SD model in this work, the derivation of the PTTA model also assumes a distribution of amplitudes of the interaction potentials and uncharacteristic lattice constants, with mean values of ⟨U0⟩ and ⟨Δx⟩, respectively. However, they are fundamentally different, as the PTTA model is independent of the statistical distributions in the amplitude of the interaction potential and slip distances, whereas the SD model strongly depends on them. Therefore, a comprehensive study comparing the application of these two models can be of merit.
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CONCLUSIONS Performing FFM experiments on a catalyst powder comprised of Fe−Al−O spinel nanoparticles resulted in a high-resolution chaotic stick−slip friction pattern. The measured lateral forces showed scaling with the applied normal load, whereas the distances between slip events did not show a particular trend. We estimated the surface corrugation energy amplitude of the catalyst from our data using two approaches, a mean version of the PT model and a statically disordered model. Each approach has its advantages and disadvantages. For instance, the mean PT model is easy to implement, compared to the other two; however, it has large errors. The SD model is more physically relevant with regard to the complexity of the surfaces and provides more concise values; however, the SD model can display some deviations in the fittings. These two approaches provided about similar values, according to which the catalyst exhibits high surface energy compared to an inert material (NaCl). One may consider the use of complementary computational methods to provide further insights into the potential of such surfaces more explicitly, such as molecular
⟨Δx⟩|FN 2π
(4)
where ⟨FL ⟩ and ⟨Δx⟩ were calculated from the measured data (Figure 3) at each normal load. Figure 5 plots the corrugation energy amplitude estimated by the PT model (purple triangles) together with the values estimated by the SD model (light blue squares), given by eq 3, scaled down by a factor of 2π (see the SI Appendix 4). The two approaches predict values within close vicinity, although the estimations of ⟨U0⟩ made by the PT model (eq 4) are more scattered than the ones obtained by the SD (eq 3) model. Extrapolating the corrugation energies to zero normal load, the PT model estimates ∼2.8 eV and the SD model estimates ∼1.2 eV. To put in perspective, these values display considerably higher surface energy compared to the 0.014 eV estimated at the zero load for NaCl measured in FFM under identical conditions (also in ethanol using the same apparatus).21 Whereas the interaction energy amplitude given max
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DOI: 10.1021/acs.jpcc.8b12085 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C dynamics simulations20,46 or ab initio calculations.50−52 The approach used in this work can be utilized for the interpretation of FFM experiments performed on materials, which are characterized by polycrystalline/amorphous surfaces or provided as powders.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b12085.
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Further details on XRD surface characterization of the catalyst sample, the derivation and underlying assumptions behind the SD model, correlation between the measurable parameters, relation between mechanical work and corrugation energy, possible application of the PTTA model, and comparison between frictional characteristics of the spinel catalyst and NaCl (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Ronen Berkovich: 0000-0002-0989-6136 Author Contributions §
L.A. and I.S. contributed equally to this work.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge the financial support by the I-CORE Program of the Planning and Budgeting Committee and The Israel Science Foundation (Grant No. 152/11). The authors are grateful to Dr. R. Vidruk-Nehemya, Prof. M. Landau, and Prof. M. Herskowitz from the Blechner Center at Ben-Gurion University of the Negev for providing us with the catalyst samples and for its XRD characterization. The COST Action MP1303 is gratefully acknowledged.
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ABBREVIATIONS FFM, friction force microscopy; AFM, atomic force microscopy; PT, Prandtl−Tomlinson; PTTA, thermally activated PT model for amorphous surfaces; SD, static disorder; XRD, X-ray diffraction; pdf, probability distribution function; cdf, cumulative distribution function
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REFERENCES
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DOI: 10.1021/acs.jpcc.8b12085 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.jpcc.8b12085 J. Phys. Chem. C XXXX, XXX, XXX−XXX
