Application of Static Disorder Approach to Friction Force Microscopy of

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

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, Jurgen Jopp, and Ronen Berkovich J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b12085 • Publication Date (Web): 18 Jan 2019 Downloaded from http://pubs.acs.org on January 22, 2019

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The Journal of Physical Chemistry

Application of Static Disorder Approach to Friction Force Microscopy of Catalyst Nanoparticles to Estimate Corrugation Energy Amplitudes Liron Agmon1, ‡, Itai Shahar1, ‡, Bat-El Birodker1, Simona Skuratovsky1, Jürgen Jopp2, and Ronen Berkovich1, 2, * 1

Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer Sheva 84105,

Israel. 2

The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the

Negev, Beer Sheva 84105, Israel. ‡ Both

authors contributed equally to the work.

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ABSTRACT

Friction force microscopy (FFM) of materials with well-defined crystalline surfaces are interpreted within the framework of the Prandtl-Tomlinson (PT) model. This model portrays the interaction with a surface through a deterministic periodic potential. 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 nanofriction measured on a catalyst with irregular surface, by describing the slip forces in terms of static disorder (SD) in the corrugation potential. Using FFM we measure powder of Fe–Al–O spinel catalyst, which is involved in reverse water-gas-shift reaction. The FFM measurements resulted with intermittent stick-slip pattern with large variance in the slip forces and in 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 FFM measurements of materials with irregular surfaces.


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INTRODUCTION Catalyst reagents are involved in chemical reaction by binding the reactants molecules into its 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 towards the desired product, which also reduces the amount of required chemical work.1 This brought to an increasing effort in studying surface phenomena and characteristics associated with catalytic performance,2-4 and 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 relate with catalytic performance.5, 9 FFM enables probing interactions in the single asperity level. In such 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 nanocrystals aggregates.22 Fe–Al–O spinel is a crystalline multi-oxide matrix, designed as a novel bifunctional catalyst for production of liquid hydrocarbon fuels and chemicals by 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) model25-26 that assumes a periodic interaction potential, which makes it


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ideal for the description and interpretation of 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 poses well defined crystalline faces, such as oxide surfaces31-35 graphene oxide,36 amorphous carbon and diamond-like carbon films37-39 etc. Facing this dilemma, different approaches were proposed, e.g. based on the local contact area,33 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 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 corrugation energy amplitude of the catalysts, and found it comparable to the mean mechanical work, and consequently with values provided by the PT model when scaled by a factor of 2π.

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 SI appendix, 1). The powder is comprised from 3 – 4 nm nanocrystals of the catalyst fused to 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, GTP16218), 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-


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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 300 stick-slip cycles (loops) were taken per each scanning velocity. AFM imaging. An Asylum Cypher-ES AFM in the AC operating mode using a sharp silicon cantilever (Olympus AC-240TS) 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 a metal coverslips.

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 does not chemisorbed. Being a metal oxide, the spinel at temperatures higher than 200-300oC, 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 in order to carry out the FFM measurements. Topographic AFM surface image of nanoparticles comprising the powder of Fe–Al–O material is


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shown in Figure 1a. This image illustrates the particle size distribution, where the nano-particle size varies from 15 – 25 up to ~ 90 nm aggregates. The blue line marks a cross-section over several catalyst particles. Figure 1b shows two FFM images, upon which zooming onto smooth 5 – 20 nm wide flat regions on the top part of the nanoparticles were identified as favourable scanning location for the FFM measurements. 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.

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, on two resolutions, 500×500 nm2 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 normal load of 12.9


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nN (top panel). Friction loop (lower panel) corresponding to the red line in the friction map above, shows an erratic stick-slip pattern.

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 (Fig. 2a), 12.9 nN (Fig. 2b) and 20.4 nN (Fig. 2c) show an irregular stick-slip pattern. The friction measurements displayed none to mild force strengthening with the scanning velocity (see SI), but showed a strong dependency with the applied normal load. As can be seen in Figure 2, under the application of higher loads the measured lateral friction forces increases together with the hysteresis between the forward and backward scans. This increase of the area confined by the two friction scan lines, qualitatively reflects that the energy dissipation increases with the 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.


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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.


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We calculated the probability distribution functions (pdfs) of the slip lateral forces, FL, and of the distances between slip events, ∆x, 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 behaviour. Figure 3a plots the maximal slip forces, FLmax, the peak value of FL just before a slip occurs, against their corresponding ∆x. The correlation between FLmax and ∆x was estimated by calculating the coefficient of determination (see SI appendix, 2) for each data set for at the applied normal load (Fig. 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 for certain slip forces with a specific periodicities. This behaviour 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, ∆x, its values are scattered, particularly under low loads. At normal loads higher than ~10 nN, the distributions of ∆x became narrower, although still displaying similar mean values around 0.47 nm with a relatively wide variance. Interestingly, the ∆x 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 well-defined crystalline structure, one would expect to observe a constant characteristic lattice parameter. However, as evident from Figs. 1c and 2, the catalyst powder measured here did not display a uniform surface, unlike purely crystalline surfaces that show a 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


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crystallographic planes with several oxidation levels of the iron ions,23 and possibly crossing grain boundaries combined.

Figure 3. Lateral friction forces and position variations distributions at different normal loads. a) Maximal lateral slip forces vs. their corresponding recorded distances between slip events, ∆x. The inset shows the calculated coefficient of determination for {FLmax} and {∆x} at each load. b) Mean values of ∆x with their probability densities as function of the applied normal load. c) Mean lateral slip force values with their probability densities as function of the applied normal load.

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 increase 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 chemical interactions within it.43-46 Such stochastic stick-slip behavior was recently reported for oxide


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surfaces,33 and was 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, describe the tipsample 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,

(1)

 2xt  , U int  xt   U 0 cos   a 

where U0 is the corrugation energy amplitude, x is the time dependant position of the tip, and a is the lattice periodicity. The second term accounts for the position and time dependent elastic deformation of the cantilever, Uel(x, t) = (Keff/2)(x - XS)2, where Keff is the effective lateral spring constant,10, 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. While this serves as a reasonable approximation for ordered crystalline surfaces with a well-defined lattice coefficient, i.e., ∆x = 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, which utilizes a modified Lennard-Jones 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 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


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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 R. Zwanzig, who described a stochastic process of barrier crossing in terms of a disordered rate governed process.4748

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 non-exponential 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 ∆x, to be disordered parameters, which can be expressed by

(2)

U 0 t   U 0  U 0 t ; x t   x  x t ,

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 ∆x is given by its decomposition into its averaged value ∆x, and the fluctuating deviations around it δ∆x(t). The interaction potential will now be given by [U0 + δU0(t)]cos[2πx/(∆x + δ∆x(t))], which is illustrated in Figure 4a, based on the force and position distributions measured at FN = 3.6 nN. 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 SI appendix, 3):


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(3)

S FL   1  e



f0

   U2 0  FL2 2x   FL   1  f 0   FL  2   k T  B   



1 2

where f0 = [f0/(Keff.V)]exp(–[(U0 – FL∆x)/kBT]) is the rate of crossing the mean barrier with units of [1/nN], f0 is the attempt frequency, σUo and σ∆x are the standard deviations of the fluctuations in U0 and in ∆x, kB is Boltzmann's constant and T is the absolute temperature. Note that when the fluctuations are minor, Eq. (3) regain an exponential dependency, which means that U0 = U0, and ∆x = ∆x. 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, ∆x, and σ∆x 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.


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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 (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).

The fittings returned f0 that vary between 0.1 to 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 results 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


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log-normal distribution of ∆x 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.∆x (see SI appendix, 4). We compared these values with predictions made by the PT model, according to which the mean corrugation amplitude can be calculated via:15

(4)

U0

FN   PT

FLmax

x FN

2

FN

where FLmax and ∆x 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 SI appendix, 4).


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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.

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 zero load for NaCl measured in FFM under identical conditions (also in ethanol using the same apparatus).21 While the interaction energy amplitude given 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 SI appendix, 5). Reflected through its surface potential, this indicates the activity of the catalyst surface compared to the 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 SI appendix, 6). Although the PTTA model relies on a different approach than the SD model presented in this work, the derivation of the PTTA model also assumes a distribution of amplitudes of the interaction potentials and uncharacteristic lattice constant, with mean values U0 and ∆x 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, while 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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CONCLUSION Performing FFM experiments on a catalyst powder comprised of Fe–Al–O spinel nanoparticles resulted in high-resolution chaotic stick-slip friction pattern. The measured lateral forces showed scaling with the applied normal load, while 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 regards 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 on the potential of such surfaces more explicitly, such as molecular 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.

ASSOCIATED CONTENT Supporting Information


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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 [email protected] (ORCID – Ronen Berkovich: 0000-0002-0989-6136) ‡ L.A.

and I.S. contributed equally.

ACKNOWLEDGMENT 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 BenGurion University of the Negev, for providing us with the catalyst samples and for its XRD characterization. The COST Action MP1303 is gratefully acknowledged.

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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TOC Graphic


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Application of Static Disorder Approach to Friction Force Microscopy of

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