Baodan Zhang

Dr Wei Wang
email: wangwei@jgsu.edu.cn

Dr Cheng Liu

Lianhuan Han

Dr Juan Peng

Dr Alexander Oleinick

Prof. Dr Irina Svir

Christian Amatore
email: christian.amatore@ens.psl.eu

Zhong-Qun Tian

Prof. Dr Dongping Zhan
email: dpzhan@xmu.edu.cn

Prof Jean-Michel Savéant

Dr Christian Amatore Pasteur

Surface Diffusion of Underpotential-deposited Lead Adatoms on Gold Nanoelectrodes

A simple and readily applicable voltammetric approach is described to characterize and measure the site-hopping surface diffusion of underpotential-deposited (UPD) metal adatoms at nanoelectrodes. UPD refers to the deposition of atoms on foreign metal supports at potentials lower than those predicted by Nernst law for a bulk deposition. Despite its importance in several fields of catalysis, advanced nanofabrication or even atomic nanoengineering by atomic layer epitaxy, diffusion of UPD adatoms is difficult to observe at micro-and macroelectrodes. In fact, at electrodes of usual dimensions, UPD adatoms surface diffusion is masked by other electrochemical phenomena of greater relative amplitudes. Conversely, at nanowires electrodes sealed in glass, only an extremely small fraction of the surface of the wires is exposed to the electrolyte solution and is rapidly loaded. This allows the spillage of UPD adatoms onto the much larger area of the nanowire rod which is immune to Faradaic reactions due to its isolation from the electrochemical solution by the glass casing. Therefore, surprisingly for a UPD process, voltammetric peaks currents and integral desorption charges primarily reflect these diffusional surface processes so that the integral charges vary linearly with the inverse of the square root of the scan rate. This is easily observable and measurable with usual bench-level electrochemical instrumentation. In this work, by using nanoelectrodes with diameters between 90 and 260 nm, we were able to establish the major involvement of this site-hopping surface diffusion of UPD Pb adatoms on polycrystalline gold (Au) and characterize it quantitatively. The equivalent surface diffusion coefficient of UPD Pb adatoms was determined to be ~4.4 × 10 - 11 cm 2 s -1 at room temperature, corresponding to a Gibbs free energy activation barrier of ca. 18.72 kJ mol -1 (i.e., 0.19 eV per Pb adatom) for the reaction of inter-sites exchange of Pb adatoms on a polycrystalline Au surface.

Introduction

UPD refers to the deposition of metal adatoms (Mad) on surface sites of different solid metal supports (Ssites) at an energy lower than that corresponding to the equilibrium potential predicted by the Nernst's law for a bulk deposit. [1] This electrochemical phenomenon occurs when Mad-Ssites interactions are stronger than M-Mbulk ones. Then, the electroreduction of free M cations (or M-containing species) into Mad adatoms on Ssites requires a less negative potential than on metallic M substrate. [2] Because M and S have different electronic work functions, the valence electron densities of Mad-Ssites bonds are not shared equally between the two moieties which therefore carry formal partial charge numbers. [3] For this reason, UPD adatoms may significantly modulate the catalytic and electrocatalytic properties of their metal supports by affecting their geometric and/or electronic structure or their surface energy. This makes them prone to play crucial roles in electrocatalysis, [4] as well as in heterogeneous catalysis (where this phenomenon is often referred to as "electron spilling" or "support effect"). [5] For example, UPD adatoms can inhibit catalyst poisoning, and may drive a reaction selectively towards a particular product, [6] or provide adsorption sites for reactive species to facilitate bifunctional catalysis. [7] Interestingly, all these effects can be finely tuned to define the ultimate properties of (electro)catalysts by taking advantage of the fact that the coverage of a substrate by UPD adatoms is generally easily controllable. [8] It should be noted in this regard that since the maximum UPD coverage of a metal substrate is necessarily limited to the formation of a monolayer of adatoms, the electrochemical charge associated to the stripping of UPD adatoms can be used effectively to determine the "real" surface area of metal catalysts. [9] UPD is also important in controlling nucleation and growth during subsequent electrodeposition processes.[10] For example, it can be used to form seed-layers to improve the quality of electroplating by controlling the binding strength between a substrate and additional plating layers. [11] This principle can even be extended to allow layerby-layer nanoengineering of crystalline and polycrystalline materials in controlled atomic layer epitaxy (ALE). [12] For example, such an electrochemical atomic layer epitaxy (EC-ALE) has been designed to nanofabricate nanofilm of CdTe semiconductor on Au(111) by alternating electrodeposition of Cd and Te atomic layers. [13] Finally, UPD metals can even be used to load non-UPD metals onto a nanostructure by resorting to replacement reactions to form core-shell nanostructures.[14] Hence, provided that all its dynamic are fully mastered at the atomic level, UPD should play an increasing role in nanofabrication or even atomic fabrications. [15] However, the observation of clusters forming by aggregation of UPD adatoms demonstrates the existence of their surface diffusion and the way in which this can alter the desired properties of the overall material.[16] A proper understanding and a quantitative characterization of the surface diffusion of UPD adatoms is therefore crucial for the success of most of the above applications. However, investigating surface diffusion of UPD adatoms is extremely difficult experimentally [17] unlike what can be done for nucleation processes during overpotential deposition (OPD).

Hereafter, we wish to validate the extreme efficiency of a simple electrochemical strategy allowing such precise investigations. At usual electrodes, surface diffusion of adatoms is masked by the greater relative magnitude of the combined effects of heterogeneous Faradaic reactions and resulting transport processes occurring in the electrolyte. Conversely, at sealed nanodisk electrodes, only a very small fraction of the surface of the metallic nanowires is exposed to the electrolyte solution and is expected to be rapidly loaded or unloaded leading to classical bell-shaped voltammograms as occurs at larger electrodes. Nonetheless, we report thereafter that in the case of UPD lead adatoms deposited on polycrystalline Au nanodisk electrodes, the Pb UPD process can extend far beyond the expected full coverage of the nanodisk surface. This is shown to be due to the spillage of UPD lead adatoms across the nanodisk edge and their ensuing site-hopping diffusion onto the cylindrical surface of the nanowire rod which is isolated from the solution by its glass casing. This phenomenon provides a simple benchlevel voltammetric method for energetically and kinetically characterizing the site-hopping surface diffusion of UPD lead adatoms onto polycrystalline Au.

Results and Discussion

Polycrystalline Au disk nanoelectrodes were prepared with a laser puller and polished by a precision sander to expose Au nanodisks as reported previously by some of us.[18] Ferrocenemethanol (FcMeOH) was adopted as the redox couple to characterize the apparent geometric size of the corresponding Au nanodisk electrodes, because its redox reaction involves a simple electron transfer mechanism and follows a well characterized diffusionlimited mass-transfer process with a diffusion coefficient of 7.8 × 10-6 cm 2 s -1 for FcMeOH in 0.1 M K2SO4. [19] Also, and more importantly for our objective in this work, an outer-sphere electron-transfer reaction would take place in this system, not involving sensible Faradaic adsorption. Accordingly, the well-defined steady-state cyclic voltammograms were obtained as typified in Fig. 1a. From the steady-state limiting current in Fig. 1a, an apparent diameter of 96 nm was determined for the examined Au nanodisk electrode. The diameters of all others nanodisk electrodes used in this study were determined by the same method and ranged between 90 and 260 nm (see, e.g., the insets in Figs. 2a-c).

v = 0.1 V s -1 to 1 V s -1 increasing in steps of 0.1 V s -1 ), T = 25°C.
Before any UPD experiment, the Au nanoelectrodes surfaces were cleaned, pretreated and activated by repetitive voltammetric cycling in 0.5 M H2SO4 solution saturated by nitrogen gas. [20] Classical voltammetric behaviors of polycrystalline Au electrode in H2SO4 were observed (Fig. 1b) denoting a clean and homogenous Au surface, where the faraday currents of water-dissociation adsorption (anodic scan) and the oxygen-adspieces desorption (cathodic scan) were well-defined as those obtained on macro-and micro-electrodes. [21] Figs. 2a-c report a series of cyclic voltammograms recorded for UPD of Pb on polycrystalline Au at three different Au nanodisk electrodes at a series of scan rates increasing from 0.1 V s -1 to 1 V s -1 in steps of 0.1 V s -1 . The inserts are the steady-state voltammograms of each nanoelectrode obtained with the same experimental conditions as described in Fig. 1a, which are employed to determine the apparent diameter of each nanoelectrodes. As it is classically obtained at Au macroelectrodes, two cathodic UPD waves were observed around at -0.55 V and -0.68 V, and two anodic stripping waves were observed around at -0.65 V and -0.38 V vs. a Hg/Hg2SO4 reference electrode with a scan rate of 0.1 V s -1 . [22] The redox peaks at (-0.68 V, -0.65 V) were assigned to the UPD Pb on Au(111) facet, and the redox peaks at (-0.55 V, -0.38 V) were assigned to the UPD Pb on Au(100) and Au(110) facets which may involve some surface reconstruction. That the potential differences of the corresponding current peaks are pretty larger than those observed at conventional Au macroelectrodes, may predict some unique behavior at Au nanoelectrode.

However, unlike with larger Au electrodes, [22,23] the charge associated with the stripping of UPD Pb adatoms was found to increase in proportion to the inverse of the square root of the scan rates (Figs. 2d-f). It should be noted that, since in our experiments the concentration of Pb 2+ is as high as 1 mM, the mass flux should be enough for the UPD reaction occurring at the Au nanodisc electrode/solution interface. On the Au macroelectrode, the current should be in proportion to the scan rate. This apparently strange behavior is nevertheless in full agreement with what some of us have already observed when studying the surface electrochemistry of platinum nanoelectrodes in sulfuric acid. [18] As previously rationalized in these previous works, this rare behavior for stripping voltammetric waves results directly from the nanometric sizes of current Au nanowires. Indeed, at a given potential, comparing with macroelectrodes, the complete loading of the extremely small surface area of the Au nanodisks that is exposed to the electrolyte solution with UPD Pb adatoms corresponds to a very low charge consumption. UPD Pb adatoms can then spill over the edge of the nanodisks and accumulate in relatively larger quantities through site-hopping propagation onto the rod surface of the nanowires as sketched in Figure 3. This latter process, equivalent to diffusion, [24] is invisible at larger usual electrodes since the UPD atoms ultimately present on the disk electrode area are then stored in much larger quantities relative to those which can spill over onto the nanowire rod due to the small values of site-hopping diffusion coefficients (see below). Yet, it becomes the dominant one that controls the Faradaic processes at nanoelectrodes. We also observed the peak potentials for the UPD and stripping processes shift with the scan rate. This quasi-reversible behavior is indeed caused by the Gibbs free energy of the surface diffusion of the UPD Pb adatoms on Au surface, which will be quantified later by the temperature-controlled experiments. nm) in an aqueous solution containing 1 mM Pb(NO3)2 and 0.1 M NaClO4 at a series of 10 scan rates in each case (from smallest to largest CV: 0.1 V s -1 to 1 V s -1 by increments of 0.1 V s -1 ). The inset in each panel reports the steady-state voltammogram recorded at the same Au nanodisk electrode in an aqueous solution containing 1 mM FcMeOH and 0.1 M K2SO4 at a scan rate of 0.1 V s -1 (compare Fig. 1a). (d-f) Linear relationship between the integral desorption charge of UPD Pb adatoms and the inverse of the square root of scan rates corresponding to the voltammograms in (a-c) respectively. T = 25°C.

Hence, at sufficiently small nanoelectrodes, the UPD Pb stripping current, i, and the corresponding stripping charge, Q, are essentially representative of the quantities of UPD Pb adatoms that were stored over the nanowire rod surface. Indeed, both i and Q vary with the square-root of the scan rate, v 1/2 , as occurs for classical linear diffusion processes, and no component proportional to the scan rate, v, as usually expected for a capacitive contribution or for the stripping of a fixed quantity of UPD Pb adatoms adsorbed on the nanodisk Au surface. [25a,b] Note that the absence of any capacitive component is perfectly normal for nanodisks of a few hundreds of a nanometer or less in the range of scan rates investigated here (compare Fig. 1a). In other words, this result implies that the quantity of UPD Pb adatoms that diffused and adsorbed by site-hopping sequences [24] along the rod flank surface of the nanowire during one voltammetric scan largely exceeds that adsorbed over the nanodisk exposed to the solution.[25c] Note indeed that the UPD Pb monolayer surface concentration on the Au nanodisk electrode surface area exposed to the solution must obey a near steady-state regime at each instant owing to the extremely small time constant, 𝜃 𝑟 /2𝐷 , of diffusional transport from the solution to the nanodisk surface where rdisk is the radius of the Au nanowire, and Dsoln the diffusion coefficient of Pb(II) species in the solution. 𝐶 has therefore to keep its saturation value, 𝐶 , i.e., 305 μC cm -2 symbolized as C* in following Eq. ( 1), [22a] while UPD Pb adatoms spill over the nanowire rod flank. Accordingly, the stripping charge may be expressed as in Eq.

(1)[18a,25]

𝑄 𝑖 𝑑𝑡 𝑛𝐹𝐷𝐶 * 2𝜋𝑟 𝜒 𝜎𝑡 𝑑𝐸 / 𝑣 / ( 1 )
where, D is the equivalent surface diffusion coefficient of UPD Pb site-hopping, [24] E1 and E2 the initial and final desorption potentials of UPD Pb, R the perfect gas constant, T the temperature, and (t) is the canonical function introduced by Nicholson and Shain. The validity of the above assumptions justifying the use of Eq. ( 1) to account for the stripping charge[25c] are confirmed a posteriori by the fact that the time constant of diffusional transport from the solution to the nanodisk surface, 𝜃 , is effectively much smaller than that, 𝜃 𝐷𝑅𝑇/ 𝑛𝐹𝑣 , of the linear diffusion of the adatoms along the Au nanowire shaft imposed by the voltammetric scan rates. Indeed, based on a series of experiments performed using several nanowire disk electrodes (see, e.g., Fig. 2), the surface diffusion coefficient of UPD Pb (D) was evaluated to be 4.4 × 10-11 cm 2 s -1 at 25 C°. This value is in fair agreement with a previous experimental estimation based on low energy electron diffraction (LEED), from which the half mean distance of atomic steps on Au was evaluated as 20 nm. [22b] An empirical Arrhenius equation is often adopted to investigate kinetic properties of surface diffusion [24c-f]:

𝐷 𝐷 exp ∆E /𝑘𝑇 (1)
where, D0 is a pre-exponential factor, ΔEd the activation energy of site-hopping reactions,[24b] k the Plank constant, and T the absolute temperature. From the linear relationship observed between lnD and 1/T (see Fig. 4f), one obtains D0 = 1.1 × 10-6 cm 2 s -1 and ΔEd = 0.19 eV (i.e., 18.72 kJ mol -1 ). Indeed, when an electrode size is reduced to nanometric scales, the relative amplitudes of the contributions of the classical phenomena of solution diffusion and Faradaic adsorption / desorption, which remain linked to the surface area of the nanodisk exposed to the solution, and that of the diffusion of adatoms along the nanowire rod of much larger surface area is reversed compared to what occurs with larger electrodes. At usual macro-or microdisks electrodes, there is essentially an involvement of charge transfers reactions coupled to diffusion of electroactive species in the solution and with the loading/unloading of UPD adatoms onto the microdisk surface area exposed to the solution. This combination of phenomena conventionally considered when it comes to large usual electrodes underlies the observation of sharp bells conventionally expected for stripping voltammetric waves. On the contrary, as soon as the size of a nanoelectrode is sufficiently small, one can observe the comparatively more important spillage of the UPD adatoms over the edge of the electroactive disc exposed to the electrolyte and their subsequent diffusion by site hopping along the atomic surface of the metallic substrate of the rod hidden from the solution by its glass casing. Indeed, due to the low magnitudes of the equivalent diffusion coefficients that is imposed by the values of activation barriers of the UPD Pb site exchange reactions onto the Au surface, this spilling phenomenon may become visible and ultimately dominates the whole electrochemical behavior only for electrodes constructed from nanowires of a few hundred nanometers or less. It is then observed that the voltammetric waves featuring the UPD loading and unloading of Pb adatoms on polycrystalline Au exhibit classical diffusional shapes and that the integral charges corresponding to the UPD Pb stripping waves vary proportionally to the inverse of the square root of the voltammetric scan rate, revealing that that surface site-hopping diffusion is the rate-determining step of the global UPD Pb process on the Au nanoelectrode. 1 M NaClO4 at a series of 10 scan rates in each case (from smallest to largest CV: 0.1 V s -1 to 1 V s -1 by increments of 0.1 V s -1 ).

Conclusion

The underpotential deposition of Pb on polycrystalline Au surface has been reexamined taking advantage of nanodisk electrodes special features associated with their extremely small sizes, as this provides new and easy access to measurements of surface diffusion of UPD Pb adatoms on polycrystalline Au with usual bench-level cyclic voltammetry. Taking advantage of this unique behavior, using simple voltammetric experiments, the apparent surface diffusion coefficient of UPD Pb adatoms on polycrystalline Au surface could be determined to be ~4.4 × 10 -11 cm 2 s -1 (at 25 C°) corresponding to an activation energy barrier of 18.72 kJ mol -1 . We believe that this simple and practical methodology based on classical voltammetric experiments performed at nanodisk electrodes will not only prove significant for kinetic investigations related to electroplating processes, but will also present several interesting applications in the sciences of nanoengineering. For example, this approach can certainly be used with great interest, especially in the fields of electrocatalysis, nanofabrication and electrochemically driven atomic-layer epitaxy, but also for the design of better heterogeneous catalysts due to the importance of surface diffusion of adatoms during the formation of reactive metal clusters and/or for preventing their inactivation due to their uncontrolled growth.

Figure 1 .

 1 Figure 1. (a) Steady state voltammogram recorded at a 96 nm diameter Au nanodisk electrode in an aqueous solution containing 1 mM FcMeOH and 0.1 M K2SO4 at a scan rate of 0.1 V s -1 (b)Cyclic voltammograms recorded at the same Au nanodisk electrode in an aqueous solution containing 0.5 M H2SO4 for a series of 10 scan rates (from smallest to largest CV: v = 0.1 V s -1 to 1 V s -1 increasing in steps of 0.1 V s -1 ), T = 25°C.

Figure 2 .

 2 Figure 2. (a-c) Cyclic voltammograms recorded at three Au nanodisk electrodes (diameters: (a) 257 nm, (b) 182 nm, (c) 239nm) in an aqueous solution containing 1 mM Pb(NO3)2 and 0.1 M NaClO4 at a series of 10 scan rates in each case (from smallest to largest CV: 0.1 V s -1 to 1 V s -1 by increments of 0.1 V s -1 ). The inset in each panel reports the steady-state voltammogram recorded at the same Au nanodisk electrode in an aqueous solution containing 1 mM FcMeOH and 0.1 M K2SO4 at a scan rate of 0.1 V s -1 (compare Fig.1a).(d-f) Linear relationship between the integral desorption charge of UPD Pb adatoms and the inverse of the square root of scan rates corresponding to the voltammograms in (a-c) respectively. T = 25°C.

Figure 3 .

 3 Figure 3. Left: Schematic representation of the double-jacket electrochemical 3-electrode cell used in this work. Center: Closeup cartoon of the tip of one of the Au nanoelectrodes placed in the 1 mM Pb(NO3)2 and 0.1 M NaClO4 thermostated bulk solution. Right: Sketch of the site-hopping equivalent linear diffusion of UPD Pb adatoms onto the Au surface of the microwire shaft (the surface is "unfolded" so that shat-disk edge contact is shown as the bottom boundary over which UPD Pb adatoms are spilling when the nanodisk surface area exposed to the solution is fully loaded; Au atoms are represented by the array of solid yellow circles in the right cartoon).

Figure 4 .

 4 Figure 4. (a-e) Linear correlations between the integral desorption charge of UPD Pb adatoms and the reciprocal of the square root of scan rate at different temperatures as indicated in each panel. (f) Arrhenius plot for the variations of the natural logarithm of the apparent surface diffusion coefficient values D of UPD Pb adatoms with the reciprocal of the temperature. All data were recorded at a 286-nm-diameter Au disc nanoelectrode in an aqueous solution containing 1 mM Pb(NO3)2 and 0.1 M NaClO4 at a series of 10 scan rates in each case (from smallest to largest CV: 0.1 V s -1 to 1 V s -1 by increments of 0.1 V s -1 ).

Acknowledgements

In China, the financial support of the National Natural Science Foundation of China (21802057, 21827802 and 22021001), the Jiangxi Education Department (GJJ190571), the Fundamental Research Funds for the Central Universities (20720190023) are appreciated by all co-authors. In Paris, this work was supported in parts by CNRS, ENS-PSL University and Sorbonne University (UMR 8640 PASTEUR). All co-authors from Xiamen and Paris groups greatly acknowledge the Sino-French LIA CNRS NanoBioCatEchem for supporting the collaboration between the two teams. All co-authors declare no competing financial interests.

Keywords: under potential deposition • Faradaic adsorption • surface diffusion • nanoelectrode • cyclic voltammetry

Experimental Section

Chemicals and materials

Ferrocenemethanol (C11H12FeO, 99%) were purchased from Alfa Aesar, sulfuric acid (H2SO4), hydrogen peroxide (H2O2), lead nitrate (Pb(NO3)2), potassium sulfate (K2SO4) and sodium perchlorate (NaClO4) were provided by Sinopharm Group Co. Ltd and used without further purification. Aqueous solutions were prepared from deionized water (18.2 MΩ•cm,Millipore,Co).

Preparation of Au disc nanoelectrodes

All Au disc nanoelectrodes used in experiment were fabricated by a laser-beam heating puller (P-2000,Sutter Co., USA).[18] A 25-μm-diameter Au wire was pulled inside a borosilicate glass capillary (Drummond Co. USA; 1.0 mm o.d., 0.2 mm i.d.). With a programmed laser puller, the middle part of the capillary was pre-thinned, and the Au wire was then sealed into the capillary under vacuum with the second heating process. The sealed part of capillary was heated, pulled and broken into two almost identical parts during heating process. After that, a 100-μm-diameter Ni wire was inserted into the capillary as electrical connector. Finally, the nanoelectrode tip was polished using a Sutter BV-10 beveller (Sutter Co., USA).

Electrochemical Measurements

Electrochemical experiments involving the Au nanodisk electrodes were performed with a Autolab workstation (PGSTAT302NC, Metrohm Autolab Co., Netherlands) in a three-electrode thermostatically controlled cell installed inside a Faraday cage at room temperature (298 K) unless stated otherwise. Solutions were purged by bubbling high-purity argon to remove the dissolved oxygen in experiments.

To determine the apparent geometric size of each Au nanodisk electrode, steady-state voltammograms were recorded in an aqueous solution containing 1 mM Ferrocenemethanol and 0.1 M K2SO4 at a scan rate of 0.1 V s -1 , with Ag/AgCl wires used as reference and counter electrodes.

Cyclic voltammetry in an aqueous solution containing 0.5 M H2SO4 was performed to judge of the surface status of the Au disc nanoelectrodes (leakage, cleanliness, electric double layer, etc.). In these experiments, a Pt plate was used as the counter electrode and Hg/Hg2SO4 (MSE) as the reference electrode in order to avoid the interference of Cl-ions (EMSE = 0.64V vs. RHE).

To determine the surface diffusion coefficient of UPD Pb on Au surface, cyclic voltammetry was performed at different scan rates using the electrochemically cleaned Au disc nanoelectrode in an aqueous solution containing 1 mM Pb(NO3)2 and 0.1 M NaClO4. In order to determine the parameters of the Arrhenius equation (D0 and ∆Ed, in Eq.2) characterizing the site-exchange apparent diffusion coefficient of UPD Pb adatoms onto the polycrystalline Au surface, these experiments were carried out at temperatures ranging from 303 K to 323 K at an interval of 5 K, by connecting the three-electrode thermostatically controlled cell to a continuous flow cryostat (Fig. 3).


Pierre Guetschel

Théodore Papadopoulo
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Fabrice Duprat

EEG signal analysis for epileptic seizure genesis study


Keara N ; Burke
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Daniella N ; Dellagiustina

Carina A ; Bennett
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Kevin J Walsh
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Maurizio Pajola
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Edward B Bierhaus
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Michael C Nolan
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William V Boynton
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Juliette I Brodbeck
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Harold C Connolly
email: connollyh@rowan.edu

William V Boynt

Jasinghege Don

Prasan Deshapriya
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Jason P Dworkin
email: jason.p.dworkin@nasa.gov

Catherine M Elde
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Dathon R Goli

Rachael H Hoover
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Erica R Jawin
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Timothy Mcco
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Patrick Michel

Jamie L Molaro
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Jennifer O Nolau
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Heather L Enos
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Dante S Lauretta
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Z Zeszut

Particle Size-Frequency Distributions of the OSIRIS-REx Candidate Sample Sites on Asteroid (101955) Bennu

Keywords: particle size-frequency distributions, power laws, rubble-pile asteroids, fragmentation ware for Imagers and Spectrometers (ISIS) and the Environmental Systems

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Particles formed from geologic processes, from dust to boulders, typically have a scale-invariant and fractal frequency versus size relationship due to the natural process of fragmentation [START_REF] Turcotte | Fractals and Chaos in Geology and Geophysics[END_REF]. This relationship can be modeled with a fractal (power-law), Weibull, exponential, or log-normal distribution, with varying success depending on the dataset.

In planetary science, the methods for calculating particle size-frequency distributions (PSFDs) are similar to those for calculating crater size-frequency distributions, which have long been used to estimate the ages of many planetary surfaces (e.g., [START_REF] Hartmann | Terrestrial, lunar, and interplanetary rock fragmentation[END_REF][START_REF] Michel | Itokawa's cratering record as observed by Hayabusa: Implications for its age and collisional history[END_REF]). The goal of determining PSFDs is often to assess candidate landing or sampling sites (e.g., [START_REF] Golombek | Size-frequency distributions of rocks on Mars and Earth analog sites: Implications for future landed missions[END_REF][START_REF] Golombek | Rock size-frequency distributions on Mars and implications for Mars Exploration Rover landing safety and operations[END_REF][START_REF] Pajola | The pebbles/boulders size distributions on Sais: Rosetta's final landing site on comet 67P/Churyumov-Gerasimenko[END_REF][START_REF] Pajola | Boulder abundances and size-frequency distributions on Oxia Planum-Mars: Scientific implications for the 2020 ESA ExoMars rover[END_REF]) and to understand the geophysical processes responsible for shaping a planetary surface (e.g., [START_REF] Miyamoto | Regolith Migration and Sorting on Asteroid Itokawa[END_REF][START_REF] Michikami | Size-frequency statistics of boulders on global surface of asteroid 25143 Itokawa[END_REF][START_REF] Mazrouei | Block distributions on Itokawa[END_REF][START_REF] Pajola | Size-frequency distribution of boulders ≥7 m on comet 67P/Churyumov-Gerasimenko[END_REF][START_REF] Pajola | Size-frequency distribution of boulders ≥10 m on comet 103P/Hartley 2[END_REF][START_REF] Connolly | Towards understanding the dynamical evolution of asteroid 25143 Itokawa: Constraints from sample analysis[END_REF]). For example, on the Moon, PSFDs have been used to understand rock breakdown and regolith evolution rates (e.g., [START_REF] Basilevsky | Survival times of meter-sized boulders on the surface of the Moon[END_REF][START_REF] Watkins | Boulder Distributions Around Young, Small Lunar Impact Craters and Implications for Regolith Production Rates and Landing Site Safety[END_REF]). PSFDs are also often used to understand impact processes, including the formation of secondary craters (e.g., [START_REF] Bart | Using lunar boulders to distinguish primary from distant secondary impact craters[END_REF][START_REF] Bart | Distributions of boulders ejected from lunar craters[END_REF][START_REF] Singer | Secondary craters from large impacts on Europa and Ganymede: Ejecta size-velocity distributions on icy worlds, and the scaling of ejected blocks[END_REF]). Much of this work is done through remote sensing by mapping and measuring particles that appear in images (apart from the Apollo samples returned to Earth, which were sieved; e.g., [START_REF] Butler | Analysis of the grain size-frequency distributions of lunar fines[END_REF]). Particles are measured either by their longest axis, their two longest axes, all three axes, or a full polygonal outline of the visible extent.

NASA's OSIRIS-REx sample return mission [START_REF] Lauretta | OSIRIS-REx: Sample Return from Asteroid (101955) Bennu[END_REF] conducted particle size measurements on asteroid (101955) Bennu. These measurements were needed to assess the feasibility of sample collection by the OSIRIS-REx Touch-And-Go Sample Acquisition Mechanism (TAGSAM; [START_REF] Bierhaus | The OSIRIS-REx Spacecraft and the Touch-and-Go Sample Acquisition Mechanism (TAGSAM)[END_REF][START_REF] Bierhaus | Bennu regolith mobilized by TAGSAM: Expectations for the OSIRIS-REx sample collection event and application to understanding naturally ejected particles[END_REF]). These measurements also enabled us to draw conclusions about the geophysical processes on Bennu and make comparisons with other planetary bodies. The importance of PSFDs became more crucial after arrival at Bennu revealed a surface dense with boulders and less sampleable material than anticipated [START_REF] Lauretta | The unexpected surface of asteroid (101955) Bennu[END_REF].

A global PSFD of Bennu's surface was calculated by DellaGiustina and Emery et al. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] using images acquired during the spacecraft's approach to the asteroid. Regional-scale (local) PSFDs were used to estimate the amount of sampleable material at four candidate sample sites on Bennu and to refine the coordinates for spacecraft targeting during the Touch-And-Go sampling maneuver [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF][START_REF] Dellagiustina | Overcoming the Challenges Associated with Image-Based Mapping of Small Bodies in Preparation for the OSIRIS-REx Mission to (101955) Bennu[END_REF]. The global and local analyses for sample-site selection relied on two assumptions: that the PSFD calculated from meter-sized particles could be extrapolated to constrain the PSFD of centimeter-sized particles, and that remotely sensed measurements could accurately reproduce ground truth measurements.

Here, we present local PSFDs from high-resolution images, in context with the global results, with particle sizes ranging in longest axis from 0.3 cm to 95 m. Our results provide insight into the differing geologic processes at work on Bennu's surface. These data were also key in the selection of Nightingale crater as the OSIRIS-REx primary site. Lastly, we comment on improvements that could be made in the future by similar missions.

Materials and Methods

Background

The OSIRIS-REx TAGSAM [START_REF] Bierhaus | The OSIRIS-REx Spacecraft and the Touch-and-Go Sample Acquisition Mechanism (TAGSAM)[END_REF] was designed to ingest particles smaller than 2 cm in the longest dimension, defined here as sampleable regolith. Larger particles would reduce the efficiency of collection (particles > 5 cm in longest dimension) or block the sampling mechanism completely (particles > 21 cm in longest dimension, [START_REF] Bierhaus | The OSIRIS-REx Spacecraft and the Touch-and-Go Sample Acquisition Mechanism (TAGSAM)[END_REF]). With the mission's requirement of returning at least 60 g of regolith from Bennu to Earth, it was imperative to map particles on the surface to identify regions of interest (ROIs). We define particles as features of positive relief with a well-defined perimeter, characterized by an elongated shadow at large phase angles (consistent with the definition in [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF]; Figure 1). Much like asteroid (162173) Ryugu [START_REF] Michikami | Boulder size and shape distributions on asteroid Ryugu[END_REF], the target of the JAXA Hayabusa2 mission, particles on Bennu have varied geomorphic characteristics and many are partially buried, which makes identifying particle perimeters difficult. Furthermore, mapping performed on lower-spatialresolution data will miss particles that can only be identified in higher-spatial-resolution images (see Figure 1). This example falls within the Nightingale region. Illumination conditions and pixel resolution are included for context. We define incidence as the angle between the light vector and the surface normal (Sun-Bennu-surface normal), emission as the angle between the observation vector and the surface normal (OCAMS-Bennu-surface normal), and phase as the angle between the light vector and observation vector (Sun-Bennu-OCAMS).

Mapped Image Datasets

Particle mapping was performed on images that were radiometrically calibrated [START_REF] Golish | Ground and in-flight Calibration of the OSIRIS-REx Camera Suite[END_REF] and registered to shape models of the asteroid and to each other [START_REF] Edmundson | Photogrammetric processing of OSIRIS-REx images of asteroid (101955) BENNU[END_REF], but not map-projected. A summary of the image datasets used is provided in Table 1. In most cases, multiple images were required to map all of the particles in a given scene, and the lowest emissionangle images were prioritized to minimize foreshortening and other projection effects. Particles were mapped on individual images first, then the particle measurement data were combined and cartographically projected onto an image mosaic for visualization.

DellaGiustina and Emery et al. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] mapped particles at a global scale (~0.42 m/px) on images taken by the OSIRIS-REx Camera Suite (OCAMS) PolyCam panchromatic imager [START_REF] Rizk | The OSIRIS-REx Camera Suite[END_REF] during the Approach phase of the mission [START_REF] Lauretta | OSIRIS-REx: Sample Return from Asteroid (101955) Bennu[END_REF][START_REF] Lauretta | Overcoming Challenges to Collect a Sample of the Early Solar System[END_REF] (Figure 2a). This image dataset allowed the OSIRIS-REx team to identify ROIs on Bennu's surface that warranted more study before being classified as candidate sample sites. As the team obtained higherresolution imagery throughout the subsequent mission phases, the size and location of the ROIs used for particle mapping varied (Figure 2b). These variations were partly driven by mission schedule-as image resolution increased, there were more particles to count. Refinements were also made to optimize sample collection and avoid unsafe terrain and large hazardous particles (boulders).

Table 1. Summary of the image datasets used for particle mapping. Image datasets are grouped by global or sample site location. The number of unique image/user pairs (when greater than 1) denotes when images were mapped by more than one user. In cases where this value does not match the total number of images mapped, a modified DBSCAN clustering algorithm was used to combine and reduce the dataset. The Detailed Survey phase [START_REF] Lauretta | OSIRIS-REx: Sample Return from Asteroid (101955) Bennu[END_REF][START_REF] Lauretta | Overcoming Challenges to Collect a Sample of the Early Solar System[END_REF] of the mission included the Baseball Diamond (BBD) imaging campaign, which provided global image data at ~0.05 m/px [START_REF] Dellagiustina | Overcoming the Challenges Associated with Image-Based Mapping of Small Bodies in Preparation for the OSIRIS-REx Mission to (101955) Bennu[END_REF][START_REF] Bennett | A high-resolution global basemap of (101955) Bennu[END_REF]. We performed detailed mapping of 16 ROIs. Analyses of these particle measurements, together with other data products and logistical information, informed the selection of four candidate sample sites, named Nightingale, Osprey, Sandpiper, and Kingfisher [START_REF] Lauretta | Overcoming Challenges to Collect a Sample of the Early Solar System[END_REF]. The particles mapped during BBD for each of the candidate sites are shown in Figure 2c.

Region

After selection of these final four candidate sites came the Reconnaissance (Recon) phase [START_REF] Lauretta | OSIRIS-REx: Sample Return from Asteroid (101955) Bennu[END_REF][START_REF] Lauretta | Overcoming Challenges to Collect a Sample of the Early Solar System[END_REF] of the mission, which included two imaging campaigns specific to particle mapping: Recon A and Recon C. Recon A mapping efforts (Figure 2d) demonstrated a notable improvement over the mapping performed during BBD due to higher image resolution with a pixel scale of 0.01 m/px, which allowed mappers to more easily discern particle edges than in BBD images, thus assisting the team in the final selection of the primary and backup sample sites: Nightingale and Osprey. Recon C mapping was only performed for Nightingale and Osprey, and the collected particle measurements helped the team confirm the presence of sampleable regolith at both sites as the pixel scale (~0.004 m) allowed for the identification of particles that could be ingested by TAGSAM (Figure 2e).

Particle Mapping Team and GIS Environment

For each mission phase, particles were manually identified by their longest axis dimension with polylines using ArcMap, part of the Environmental Systems Research Institute's (ESRI) [START_REF]ArcGIS Desktop: Release 10[END_REF] geospatial information system (GIS) software. The GIS environment enabled us to explore the geospatial connection between the mapped particles and the geometry layers, included as backplanes in a multilayer image cube file, using the Integrated Software for Imagers and Spectrometers 3 (ISIS3) [START_REF] Keszthelyi | Support and future vision for the integrated software for imagers and spectrometers (ISIS)[END_REF]. Pixel backplane values were assigned using ISIS3 s spiceinit routine and the approved shape model version in use in each mission phase. The values were refined using manual and automated photogrammetric registration [START_REF] Edmundson | Photogrammetric processing of OSIRIS-REx images of asteroid (101955) BENNU[END_REF]. Particle long-axis length was calculated using the Cartesian distance formula with the endpoints determined from the geometry backplanes. The decision to measure particles only by longest axis dimension was due to the tight operational schedule, which could not accommodate the increased time needed to map more detailed particle shapes.

The membership of the particle mapping team changed over the course of the mission. As a result, the team composition was not consistent across mission phases or sample site regions. To account for the uncertainty introduced by different mappers [START_REF] Robbins | The variability of crater identification among expert and community crater analysts[END_REF], we developed mapping criteria for identifying particles and relied on expert verification of all mapped images. After a member of the particle mapping team completed an image, an expert mapper reviewed the image to evaluate whether all visible particles ≥4 pixels across were identified and to remove any incorrect identifications. Generally, a minimum of 4 pixels across is required to identify a feature [START_REF] Nyquist | Certain Topics in Telegraph Transmission Theory[END_REF]. Where there was overlap between mappers on images, we employed a modified DBSCAN [START_REF] Ester | A Density-based algorithm for discovering clusters in large spatial databases with noise[END_REF] clustering algorithm to combine and reduce the dataset.

We used the GIS environment to calculate the reference surface area of each mapped region from shape models of Bennu. This value allows us to derive a cumulative frequency of particles normalized by area, providing the ability to make meaningful comparisons among regions with varying sizes of mapped areas. The shape models created for Bennu represent the surface with triangular facets where each vertex has a body-fixed Cartesian coordinate [START_REF] Barnouin | Shape of (101955) Bennu indicative of a rubble pile with internal stiffness[END_REF][START_REF] Barnouin | Digital terrain mapping by the OSIRIS-REx mission[END_REF]. The high-resolution (5-cm grid spacing) regional models are uniformly spaced grids of height values above a planar surface averaged over the region. They were converted to triangular facets using the gridded heights as vertices. To calculate surface area, we identified all facets intersecting the mapped image set. Since the shape is uniformly spaced on a projected plane, all facets have the same projected area. We report the projected grid areas of the facets with points falling within the surface area mapped. This process avoids having the facet resolution and small-scale tilts affect the computed surface area.

Evaluating Particle Measurements and Calculating the PSFD

To assess the completeness of the particle measurements and to make predictions about the proportion of unresolved fine-particulate material at a given ROI, we calculated the PSFDs and their best fit distribution. Relying on the assumption that PSFDs calculated from meter-sized particles could constrain the PSFDs of centimeter-sized particles due to their fractal frequency versus size relationship, we used a fractal distribution (a power law) to model PSFDs of Bennu. Previous work has demonstrated that this is an acceptable assumption [START_REF] Rodgers | Methodology for finding and evaluating safe landing sites on small bodies[END_REF], and DellaGiustina and Emery et al. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] showed that a power law provides a reasonable fit to the global cumulative PSFD of Bennu. Power-law fits are common in planetary science because the straightforward relationship allows for streamlined analysis and comparison with other planetary bodies (e.g., [START_REF] Golombek | Size-frequency distributions of rocks on Mars and Earth analog sites: Implications for future landed missions[END_REF][START_REF] Mazrouei | Block distributions on Itokawa[END_REF][START_REF] Pajola | Size-frequency distribution of boulders ≥7 m on comet 67P/Churyumov-Gerasimenko[END_REF][START_REF] Dombard | Boulders and ponds on the Asteroid 433 Eros[END_REF][START_REF] Krishna | Impact spallation processes on the Moon: A case study from the size and shape analysis of ejecta boulders and secondary craters of Censorinus crater[END_REF][START_REF] Küppers | Boulders on Lutetia[END_REF][START_REF] Thomas | Shoemaker crater as the source of most ejecta blocks on the asteroid 433 Eros[END_REF]). Power-law PSFDs have the form

N C = cD -a , (1)
where N C is the cumulative number of particles greater than or equal to D per surface area unit, D is the longest axis particle measurement, a is the power-law index, and c is the coefficient of proportionality.

We can also evaluate PSFDs by plotting the binned frequency of particle measurements as opposed to the cumulative unbinned frequency. This is referred to as a differential frequency plot. We can fit a power law to the differential frequency data that has the form

dN/dD = kD -b , (2)
where dN/dD is the number of particles in the given size bin per surface area, b is the power-law index, and k is the coefficient of proportionality. As the differential frequency plot is the derivative of the cumulative frequency plot, these two power-law fits are connected through their exponent, and, therefore, we expect b = a + 1, though this is rarely seen in practice due to variation within naturally occurring phenomena such as particle size. In this work, we use bin widths that progressively increase by √ 2 m, with the first bin edge starting at 0.2 cm. This allows us to account for the disproportionate number of particles at small scales.

A third way to evaluate PSFDs involves plotting the differential frequency normalized by a power law with an index of -3. This is known as a relative frequency or R plot. This type of plot can be used to gauge the spatial density of a given particle size bin. Here, we use the same binning scheme as the differential frequency plot. For crater size-frequency distributions, this type of plot is used to evaluate the level of crater saturation (e.g., [START_REF] Hartmann | Does crater "saturation equilibrium" occur in the solar system?[END_REF]).

In a double-logarithmic plot, a power law appears as a straight line, where the slope of the line is equal to the power-law index. Power laws are generally fit between a given particle-size range as smaller particles tend to be undersampled. The smallest meaningful measurement in the data set defines the completeness limit. In a double-logarithmic plot, this value often occurs where the particle measurement data appear to 'roll over' and depart from the power-law fit, but not always. This limit may or may not be a real attribute of the PSFD. Ultimately, it is constrained by image spatial resolution limits, human factors in identifying small features, and illumination conditions (which can reduce edge contrast) [START_REF] Rodgers | Methodology for finding and evaluating safe landing sites on small bodies[END_REF][START_REF] Michael | Planetary surface dating from crater size-frequency distribution measurements: Partial resurfacing events and statistical age uncertainty[END_REF].

We use the Clauset et al. [START_REF] Clauset | Power-Law Distributions in Empirical Data[END_REF] technique for fitting a power law and identifying the completeness limit. In this method the completeness limit is determined using the Kolmogorov-Smirnov statistic, minimizing the difference between the data and the best-fit power law. Then, the power-law index is determined by method of maximum likelihood. Uncertainty for both of these values is the standard error, determined through a non-parametric bootstrap. DeSouza et al. [START_REF] Desouza | Improved techniques for size-frequency distribution analysis in the planetary sciences: Application to blocks on 25143 Itokawa[END_REF] demonstrated the improved performance of the Clauset et al. [START_REF] Clauset | Power-Law Distributions in Empirical Data[END_REF] technique for PSFDs calculated for asteroid Itokawa.

We also assume that particle frequency follows a Poisson detection distribution as suggested by the Crater Analysis Techniques Working Group [START_REF]Standard techniques for presentation and analysis of crater size-frequency data[END_REF]. This assumption allows us to capture the uncertainty in particle frequency by plotting the square root of N C for each particle measurement. Presenting our results in this manner facilitates comparison with previously calculated PSFDs of other solar system bodies.

Connecting Remotely Sensed Measurements to Ground Truth

To evaluate our assumption that remotely sensed measurements could accurately reproduce ground truth measurements, we prepared analog surface rock trays with predetermined PSFDs described by power laws with indices between -3 to -2 to conduct a small laboratory study. Rocks were manually layered in several trays from largest to smallest, glued in place, and spray-painted matte black to simulate asteroid surface conditions. We imaged these trays to simulate illumination conditions with 40 • incidence (angle between the light vector and the surface normal, i.e., Sun-Bennu-surface normal), 0 • emission (angle between the observation vector and the surface normal, i.e., OCAMS-Bennu-surface normal), and 40 • phase (angle between the light vector and observation vector, i.e., Sun-Bennu-OCAMS) to provide a test data set for remote measurements. Nearly every mapper involved in our study (13 total) mapped particles in at least one of the trays to determine the accuracy of their remotely sensed particle measurements as compared to ground-truth caliper measurements (Figure 3). The team mapped the particles in these trays at different points in the mission, resulting in varying levels of detail. An initial group tested mapping and data flow processes with one of the tray images prior to the OSIRIS-REx spacecraft's arrival at Bennu. A second group of mappers performed this task after mapping particles on Bennu. The two groups differed only in the total number of mapped particles identified per mapper, where experience with mapping on Bennu led to an increased number of particle identifications in the rock tray. It is worth re-iterating that all particle mapping performed on Bennu was verified by at least one independent, experienced mapper.

We collected 85 caliper measurements from a random subset of the particles within the tray by viewing the tray from an approximately nadir position (camera pointed directly down, centered over the tray such that the lens is parallel with the plane of the rock tray) and then measuring the visible longest axis. Two separate mappers performed this step, averaging the results to obtain ground truth. Then, we manually clustered the 'remotely sensed' particles in ArcMap based on spatial location to compare with these ground truth caliper measurements. We estimated particle lengths using the image pixel scale, which we then compared to the ground truth caliper measurements (Figure 4). We found that a majority of particles (~68%) were underestimated in size by the remotely-sensed mapping. For the most part this difference was small, with ~69% of particle measurements falling within 5% error of the ground truth measurement and ~89% of particle measurements falling within 20% error of the ground truth measurement. We also compared the PSFDs between the two measurement sets (Figure 5). The power-law fits applied to the data have similar completeness limits, but the power-law index for the remotely sensed data is shallower than that of the ground truth data, though it falls within the uncertainty. Given that these power-law uncertainties overlap, we cannot conclusively state whether a measurement bias exists or would be strong enough to impact the PSFD determined through remotely-sensed measurements.

Results

The global set of particle measurements from the OSIRIS-REx Approach phase presented in DellaGiustina and Emery et al. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] included 3136 unique particles (Figure 2a). We identified between 269 and 556 unique particles for each of the candidate sample sites during BBD (Figure 2c) and between 5111 and 17,867 unique particles during Recon A (Figure 2d). During Recon C (Figure 2e), we identified 26,171 unique particles at Nightingale and 28,929 unique particles at Osprey. Using the approach described in Section 2, we calculated the PSFDs and identified the best-fitting power laws, which involved determining the completeness of each dataset. Table 2 summarizes the particle mapping effort performed during each mission phase and the resulting best fit power-law parameters. Figure 6 presents the cumulative PSFDs of the four candidate sample sites as calculated for BBD, Recon A, and (only Nightingale and Osprey) Recon C.

Table 2. Summary of particles mapped for each of the four candidate sample sites at various mission phases. Recon C mapping was only performed for the primary and back-up sample sites, Nightingale and Osprey. The surface area mapped for the global set of particle measurements has been updated from that reported in DellaGiustina et al. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF]. Unlike [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] we included the Roc (95 m) which slightly improved the estimated completeness limit. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] is included as a reference. Light gray points indicate particle measurements that were smaller than the completeness limit.

Region

The global PSFD of Bennu from DellaGiustina and Emery et al. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF], which included particles measuring between 1 and 58 m in longest axis with a best fitting power-law index of -2.9 ± 0.3 applying for particles 8 m and larger, is included for reference with a correction to the value used for area normalization to reflect the true surface area mapped as opposed to the surface area of the full global surface. We also updated these particle measurements to include the Roc (95 m; the largest cogent feature on the surface), which was previously excluded as its full particle extent could not be ascertained in lower-resolution imagery.

The power-law indices of the candidate sample sites across different mission phases suggests the use of the global PSFD to constrain expectations for site-specific PSFDs was reasonable, despite local variability. The power-law fit to the global set of measurements consistently overestimated the number of small particles present at each of the candidate sample sites. This observation is not surprising given that power-law fits are only applicable for particle sizes larger than the completeness limit and these four candidate sample sites were selected for their relative scarcity of large (hazardous) particles. However, the global power-law index provides an upper bound for all four-local power-law indices. The uncertainties in the power-law indices obtained for particles mapped during BBD are relatively high, likely as a consequence of the proportionally fewer counts; less than 600 particles were identified for each candidate sample site. At the time, these datasets were sufficient for mission operational decisions by making relative comparisons and assuming consistent mapping coverage.

Based on the detailed mapping performed during Recon A, we see a shallower powerlaw index for Nightingale (-2.3 ± 0.1), Kingfisher (-2.5 ± 0.1), and Sandpiper (-2.6 ± 0.2), whereas Osprey (-3.0 ± 0.2) has a power-law index closer to that of the global surface (-2.9 ± 0.3). However, accounting for uncertainty in the power-law index, the PSFD power-law fits determined for Sandpiper and Kingfisher fall within the uncertainty of the PSFD power-law fit determined for global Bennu. Recon C measurements produced PSFDs with similar power-law indices to those calculated for Recon A for Nightingale (-2.2 ± 0.1) and Osprey (-2.7 ± 0.6), yet both distributions visibly depart from the power-law fit (the distribution is more curved than linear), suggesting that a single power law may not fully describe the distribution of particles in these regions at this scale. In particular, the large uncertainty in Osprey's power-law index supports this conclusion. A similar effect was observed on asteroid Itokawa for particle sizes smaller than 1 m [39] and comparable trends have been observed on other bodies (e.g., [START_REF] Golombek | Rock size-frequency distributions on Mars and implications for Mars Exploration Rover landing safety and operations[END_REF][START_REF] Golombek | Size-frequency distributions of rocks on the northern plains of Mars with special reference to Phoenix landing surfaces[END_REF][START_REF] Pajola | Abundance and size-frequency distribution of boulders in Linné crater's ejecta (Moon)[END_REF][START_REF] Schröder | The Boulder Population of Asteroid 4 Vesta: Size-Frequency Distribution and Survival Time[END_REF]).

Plotting the same data in the differential frequency version of the PSFD plot (Figure 7) shows that the completeness limit identified through the Clauset et al. [START_REF] Clauset | Power-Law Distributions in Empirical Data[END_REF] method only aligns with the peak of the differential frequency data in the case of BBD, which had the smallest number of particle measurements. The Clauset et al. [START_REF] Clauset | Power-Law Distributions in Empirical Data[END_REF] technique identifies a completeness limit that maximizes the goodness of fit for the resulting power-law function. Thus, we cannot use this limit to distinguish between observation bias (e.g., image resolution) and physical processes (e.g., size sorting) as the cause for PSFDs departing from the power-law fit at small particle sizes. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] is included as a reference. Light gray points indicate particle measurements that were smaller than the completeness limit.

The Recon C Osprey PSFD exhibits distinct behavior when plotted in relative frequency (Figure 8). For the global measurements and all measurements performed at Nightingale, Sandpiper, and Kingfisher, relative frequency (R) values level off, with R around 0.4. Kingfisher exhibits a slight increase in relative frequency with the peak occur-ring around an R of 0.5. Osprey, however, does not level off; its R exceeds 1 for particles measured in Recon C images. It appears that Osprey is geometrically saturated with particles measuring between 10 and 30 cm in longest axis. This is further discussed in Section 4.2. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] is included as a reference. Light gray points indicate particle measurements that were smaller than the completeness limit.

For discussion purposes, we also present merged datasets in the cumulative PSFD plot type. We present this in two stages for clarity: a merged dataset for each mission phase (Figure 9) and a single merged dataset (Figure 10). To obtain a merged dataset for each mission phase, we combined the counts made for each of the candidate sample sites and normalized by their cumulative area. Then, to obtain a single merged dataset, we combine counts as follows: the minimum measurement from Recon C to the largest measurement smaller than the completeness limit for merged Recon A, the completeness limit for merged Recon A to the largest measurement smaller than the completeness limit for the global counts, and the completeness limit for the global counts to the Roc (95 m). We exclude merged BBD as the counts in this size range are better captured by the merged Recon A data. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] is included as a reference. Light gray points indicate particle measurements that were smaller than the completeness limit. The goal of this presentation is to simplify variation among the different sites and present a single, representative PSFD of Bennu. Though interesting for discussion, this PSFD likely represents only the lower bound of Bennu's full surface particle frequency distribution as each of the sample sites was chosen for its scarcity of large particles. Notably, this dataset is lacking in measurements between 3 to 7 m, which can be attributed to the way data was culled from the four mission phases in our analysis to produce the single merged dataset, which prioritized the completeness of measurement data. The power-law index of the single merged dataset is -2.5 ± 0.1.

Particle densities also vary across each of the four sites. In Recon A we observed particle densities (particles per square meter) for Nightingale, Osprey, Sandpiper, and Kingfisher to be 1.4, 2.0, 2.1, and 2.9, respectively, for particles greater than 30 cm. For Recon C, Nightingale and Osprey had particle densities of 6.0 and 24.7, respectively, for particles greater than 15 cm. Particle density also varied within each of the four sample sites, as evidenced in Figure 2b. For example, the area directly south of the Recon C ROI for Nightingale would have increased particle density based on the presence of the four large particles alone. The team calculated particle densities and localized power-law fits within each of the sample sites in order to optimize potential sample coordinates to prioritize spacecraft safety and the likelihood of sampling success. The relatively low particle density of Nightingale was one reason this site was ultimately chosen for sampling.

Discussion

Properties of Bennu Discernable from the PSFDs

On the basis of Bennu's relatively shallow global power-law index, the observation of very large, intact particles, and comparisons with asteroids (25143) Itokawa and (162173) Ryugu, DellaGiustina and Emery et al. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] proposed that the largest particles (boulders ≥20 m) on Bennu's surface were left over from the catastrophic parent body disruption [START_REF] Walsh | Craters, boulders and regolith of (101955) Bennu indicative of an old and dynamic surface[END_REF][START_REF] Michel | Collisions and Gravitational Reaccumulation: Forming Asteroid Families and Satellites[END_REF][START_REF] Michel | Collisional formation of top-shaped asteroids and implications for the origins of Ryugu and Bennu[END_REF] and that smaller particles (<20 m) were likely broken down by surface impacts [START_REF] Ballouz | Bennu's near-Earth lifetime of 1.75 million years inferred from craters on its boulders[END_REF] and degradation processes due to thermal fatigue [START_REF] Delbo | Thermal fatigue as the origin of regolith on small asteroids[END_REF][START_REF] Molaro | Thermal Fatigue as a Driving Mechanism for Activity on Asteroid Bennu[END_REF]. With the detailed mapping performed for the candidate sample sites during Recon A and the primary and backup sites (Nightingale and Osprey) during Recon C, we further analyze the processes responsible for the generation and degradation of smaller particles. However, given that the four candidate sample sites were chosen specifically for their expected higher-thanaverage abundance of sampleable regolith, the geophysical processes active at these sites may not be representative of those active across the global asteroid surface.

Processes observed on Bennu include space weathering [START_REF] Dellagiustina | Variations in color and reflectance on the surface of asteroid (101955) Bennu[END_REF]; thermal fracturing [START_REF] Molaro | Thermal Fatigue as a Driving Mechanism for Activity on Asteroid Bennu[END_REF]; impact cratering at large [START_REF] Walsh | Craters, boulders and regolith of (101955) Bennu indicative of an old and dynamic surface[END_REF][START_REF] Bierhaus | Impact craters on Bennu: Their morphology, size-frequency distribution, and correlation with other data sets[END_REF] and small [START_REF] Ballouz | Bennu's near-Earth lifetime of 1.75 million years inferred from craters on its boulders[END_REF] scales; mass movement due to surface slope changes, which likely results in abrasion and breakdown at large scales and equatorial deposition [START_REF] Jawin | Global Patterns of Recent Mass Movement on Asteroid (101955) Bennu[END_REF]; and particle ejection events [START_REF] Lauretta | The unexpected surface of asteroid (101955) Bennu[END_REF][START_REF] Hergenrother | Introduction to the Special Issue: Exploration of the Activity of Asteroid (101955) Bennu[END_REF]. Each of these physical mechanisms can result in particle fragmentation, thereby influencing the PSFD observed for particles at different size ranges. In early observations of Bennu, DellaGiustina and Emery et al. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] found evidence of a multimodal particle population having distinct normal albedo ranges and PSFDs. Recent work has confirmed the presence of at least two distinct particle populations on the basis of spectral, geomorphologic [START_REF] Dellagiustina | Variations in color and reflectance on the surface of asteroid (101955) Bennu[END_REF], and thermal [START_REF] Rozitis | Asteroid (101955) Bennu's weak boulders and thermally anomalous equator[END_REF] analyses: (i) a high-reflectance, high-thermal-inertia population of smooth, angular particles, all of which are smaller than ~20 m, and (ii) a more common low-reflectance, low-thermal-inertia population of rough, hummocky particles that spans the full-size range of measured objects (up to ~100 m). Both are present within the candidate sample sites (Figure 11) [START_REF] Golish | A high-resolution normal albedo map of asteroid (101955) Bennu[END_REF] suggesting that Bennu's heterogeneity [START_REF] Dellagiustina | Variations in color and reflectance on the surface of asteroid (101955) Bennu[END_REF] extends to small scales (<1 m). This heterogeneity likely influences the observed PSFD as fragmentation may affect the two particle populations on different time scales. Each of the candidate sample sites are situated within an impact crater [START_REF] Lauretta | Overcoming Challenges to Collect a Sample of the Early Solar System[END_REF][START_REF] Walsh | Craters, boulders and regolith of (101955) Bennu indicative of an old and dynamic surface[END_REF][START_REF] Bierhaus | Impact craters on Bennu: Their morphology, size-frequency distribution, and correlation with other data sets[END_REF], which likely influenced the PSFD in the region. Turcotte [START_REF] Turcotte | Fractals and Chaos in Geology and Geophysics[END_REF] compiled the power-law indices of common terrestrially fragmented objects, with most types of fragmentation resulting in a power-law index between -2.0 and -3.0. The power-law indices identified for the candidate sample site PSFDs generally fall within this range. Nightingale's power-law index is the closest to -2.0 of the four candidate sample sites (on the basis of Recon A and Recon C PSFDs). Power-law indices closer to -2.0 have been associated with timedependent disaggregation (as opposed to impact-generated disaggregation; [START_REF] Hartmann | Terrestrial, lunar, and interplanetary rock fragmentation[END_REF]); however, it is not clear that this type of process is what drives the PSFD at Nightingale given the low gravity environment of Bennu and the geomorphological setting of the site. Indeed, Nightingale is situated within a freshly exposed crater [START_REF] Dellagiustina | Variations in color and reflectance on the surface of asteroid (101955) Bennu[END_REF] and thus would be expected to have a power-law index indicative of recent impact cratering (between -2.5 to -3.0; [START_REF] Hirata | Secondary craters of Tycho: Size-frequency distributions and estimated fragment size-velocity relationships[END_REF]). This potential discrepancy in interpreting the geologic processes present at Nightingale based on the obtained power-law index, whether due to the relatively young age of the crater or specific local properties of the underlying site, will be resolved following analysis of the returned sample.

On the other hand, Osprey is closest to -3.0, a value which Hartmann [START_REF] Hartmann | Terrestrial, lunar, and interplanetary rock fragmentation[END_REF] attributed to grinding and compound fragmentation processes. Osprey is a redder-than-average crater and thus also hypothesized to be geologically young [START_REF] Dellagiustina | Variations in color and reflectance on the surface of asteroid (101955) Bennu[END_REF]. Though its power-law index is in line with the expectations for a surface that experienced impact cratering, Osprey's location on the equatorial ridge implies that equatorial deposition [START_REF] Jawin | Global Patterns of Recent Mass Movement on Asteroid (101955) Bennu[END_REF] has likely influenced the particle distribution, perhaps explaining the overabundance of particles between 10 and 30 cm in longest axis as compared to the other sites.

Using the merged datasets presented in Figures 9 and10, we can also attempt to translate these PSFDs based on particle diameter into PSFDs based on particle surface area assuming a notional boulder ellipticity of 0.7 [START_REF] Biele | macroporosity and grain density of rubble pile asteroid (101955) Bennu[END_REF]. The goal of this presentation is to understand what the average boulder surface area size would be on Bennu. This value also has implications for interpreting cratering regimes on asteroids [START_REF] Tatsumi | Cratering efficiency on coarse-grain targets: Implications for the dynamical evolution of asteroid 25143 Itokawa[END_REF]. In Figures 12 and13 we present the merged PSFDs of particle surface area with the y-axis scaled to fractional coverage. Average particle measurements (where cumulative surface coverage reaches 50%) is between 12 to 18 cm in longest axis based on the merged datasets of Recon A and Recon C (Figure 12) or is 23 cm based on the single merged dataset (Figure 13). These results could be refined by determining the true average ellipticity of particles on Bennu. Notably, the fractional surface coverage estimated in Figure 13 exceeds 1, which we attribute to overestimating particle size with ellipses (many particles on Bennu are angular) as well as measurements of partially buried particles. [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] is included as a reference. Light gray points indicate particle measurements that were smaller than the completeness limit. The black line denotes where 50% surface coverage is achieved. For each of the cumulative PSFDs (Figure 6), particle measurements depart from the power-law fit at small scales. This indicates that there is either an identification bias or a depletion mechanism affecting the frequency of smaller particles within the candidate sample sites based on a fractal frequency nature of particles. An identification bias could be systematic as a result of mappers not being able to identify features at the image resolution limit. For Recon A, this would roughly translate to 4-cm particles. In every case, however, this minimum resolvable feature size is much smaller than the completeness limits we identified with the Clauset et al. [START_REF] Clauset | Power-Law Distributions in Empirical Data[END_REF] technique. This is not surprising as the Clauset et al. [START_REF] Clauset | Power-Law Distributions in Empirical Data[END_REF] technique aims to maximize the goodness of fit between the power-law and the data set above a given particle size; however, it means we cannot differentiate between identification bias and a possible small particle depletion mechanism.

Comparison to Ryugu

Michikami et al. [START_REF] Michikami | Boulder size and shape distributions on asteroid Ryugu[END_REF] similarly found that the power-law index becomes shallower as particle sizes decrease for five localized regions on Ryugu. These five regions had power-law fits with indices between 1.65 and 2.07, thus indicating there is a lesser degree of fragmentation on Ryugu than is observed on Bennu (see [START_REF] Hartmann | Terrestrial, lunar, and interplanetary rock fragmentation[END_REF][START_REF] Thomas | Shoemaker crater as the source of most ejecta blocks on the asteroid 433 Eros[END_REF]). Michikami et al. [START_REF] Michikami | Boulder size and shape distributions on asteroid Ryugu[END_REF] noted that this observation conflicted with the high number density of large particles, which suggests that a high degree of fragmentation occurred during catastrophic disruption of the parent body, and attributed it to particle burial, which could result in a shallower power-law index.

Particle burial has also been observed on Bennu either as regolith grains overlaying larger particles or as densely packed, similar-sized particles [START_REF] Jawin | Global Patterns of Recent Mass Movement on Asteroid (101955) Bennu[END_REF]. The latter is visible at Osprey, which appears more densely packed with large particles than Nightingale (Figure 14). This is reflected in the relative frequency plot shown in Figure 8, which suggests that a physical process, such as particle saturation, is influencing the observable PSFD at this location. Examples of particle saturation are scarce in the space science literature despite the interest received by craters (e.g., [START_REF] Hartmann | Does crater "saturation equilibrium" occur in the solar system?[END_REF][START_REF] Turrini | The primordial collisional history of Vesta: Crater saturation, surface evolution and survival of the basaltic crust[END_REF]), but this is likely due to the limited availability of high-resolution images across rubble-pile bodies. Michikami et al. [START_REF] Michikami | Boulder size and shape distributions on asteroid Ryugu[END_REF] observed particle saturation in the five local sites studied on Ryugu, though the observed R values (~0.1-0.2) are slightly shallower due to the particle range being larger. It remains to be seen whether particle saturation (assuming it is present) is unique to rubble-pile asteroids such as Bennu and Ryugu, or if there is simply a lack of observations from analog features (e.g., lag deposits) on larger planetary bodies. Recently, Grott et al. [START_REF] Grott | Macroporosity and Grain Density of Rubble Pile Asteroid (162173) Ryugu[END_REF] proposed that Ryugu's PSFD is better described by a Weibull distribution of the form N(D) = N T exp(-3(D/λ) β /β),

where D is the mean horizontal particle diameter, N T is the total number of particles, and λ and β define the Weibull shape. A Weibull distribution provides an improved fit to the small diameters and is better able to capture changes in the PSFD over a larger range of particle sizes. Other studies have also proposed Weibull distributions or an exponential variation as opposed to a power-law fit (e.g., [START_REF] Golombek | Size-frequency distributions of rocks on Mars and Earth analog sites: Implications for future landed missions[END_REF][START_REF] Golombek | Rock size-frequency distributions on Mars and implications for Mars Exploration Rover landing safety and operations[END_REF][START_REF] Pajola | Abundance and size-frequency distribution of boulders in Linné crater's ejecta (Moon)[END_REF][START_REF] Schröder | The Boulder Population of Asteroid 4 Vesta: Size-Frequency Distribution and Survival Time[END_REF][START_REF] Mastropietro | Boulder Analysis on the Oxia Planum ExoMars 2022 Rover Landing Site: Scientific and Engineering Perspectives[END_REF]. Using the merged dataset presented in Figure 10, we fit a Weibull distribution (Figure 15) and, similarly, find this fit very suitable. In terms of applicability for future missions undertaking similar particle mapping work, the power-law fitting technique provides a superior estimate for gauging the completeness of measurements by providing an upper bound or conservative estimate of the completeness limit based on the fractal nature of particles; however, a Weibull fit may be a better predictor of overall particle frequency.

Limitations of the Rock Tray Study

Although the rock tray study is helpful for evaluating the accuracy of remote measurements, there are limitations to the conclusions we can draw for the PSFDs calculated for Bennu. Most importantly, we conducted the rock tray analysis with a relatively small sample size (n = 85) when compared to the number of particles measured at the candidate sample sites on Bennu (n ≥ 269). Considering that the lower particle counts from BBD images were poor indicators of later PSFDs calculated with higher-resolution data, we are hesitant to conclude that a measurement bias would be as pronounced, or even present, for particles mapped on Bennu. Additionally, the two distinct particle populations [START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF][START_REF] Dellagiustina | Variations in color and reflectance on the surface of asteroid (101955) Bennu[END_REF] on Bennu may have different measurement uncertainties due to their different physical properties. Higher-contrast boulders (bright and very dark particles) are easier to detect against Bennu's average terrain and thus likely do not suffer from as many missed detections as particles with average reflectance. Angular and smooth particles likely have improved accuracy and consistency between mappers in terms of identifying the longest axis and particle edges correctly, relative to the rougher and more hummocky particles. The rock tray study does not account for these factors. Similarly, as the rock tray study was developed in the Earth gravity environment, it does not account for patterns due to particle reorganization in Bennu's micro-gravity environment. For simplicity, we assumed that mappers would correctly identify the longest axis of particles a majority of the time. This assumption only holds true if, for a majority of particles, gravity orients the particles such that the longest axis is visible to the mapper from a roughly nadir viewing position and if mappers are able to correctly discern the longest particle axis. Michikami et al. [START_REF] Michikami | The shape distribution of boulders on Asteroid 25143 Itokawa: Comparison with fragments from impact experiments[END_REF] demonstrated that on Itokawa, smaller particles were generally oriented with the smallest axis measurement (c-axis) perpendicular to the surface, whereas larger particles were more likely to resist gravity-or friction-induced orientation. A more thorough study should be conducted to fully assess the extent of potential measurement bias that may be present in remotely sensed particle measurements. Nonetheless, the controlled study performed here highlights the types of errors that may be introduced when working with remotely sensed images of particles on a planetary surface.

Conclusions

Particle measurements enable quantitative comparisons with other planetary surfaces, influencing the conclusions that can be drawn about the geophysical processes that cause fragmentation and disaggregation on those surfaces. Though an individual power-law fit to a PSFD cannot solely convey the geologic history, in tandem with other evidence, we used these data to make inferences on the origin of surface particles. Each of the four candidate Bennu sample sites likely experienced complex particle fragmentation as a result of multiple processes and appears to have a distinct geologic history.

We identified over 100,000 particles ≥ 1 cm in the longest axis dimension across the four candidate sample sites of the OSIRIS-REx mission. On the basis of PSFD power-law indices, we infer that the primary sample site, Nightingale, is characterized more closely by processes related to disaggregation in spite of its geologically recent impact cratering history, though this cannot be fully resolved without a returned sample. Osprey maintains a PSFD consistent with its geologically recent impact cratering history except for a saturation of particles between 10 and 30 cm that could be due to equatorial deposition.

We validated our assumption that the PSFD calculated from meter-sized particles could constrain the PSFD of centimeter-sized particles, though this assumption may not hold for other localized regions on the asteroid or other planetary bodies. We determined, that at least on Bennu, particle sample sizes must be large (>600 particle measurements, likely closer to thousands) to effectively estimate particle frequency at small scales when using a power-law model. The Weibull distribution appears to be a better predictor of particle frequency than power-laws, though smaller sample sizes of particle measurements could lead to an underestimation of the frequency of smaller particles. In practice, it may be best to use both of these distributions to model the full range of potential PSFDs.

Through our laboratory study to connect ground truth measurements to remotely sensed measurements, we found that a possible systematic bias present for remotely measured particles may cause smaller particles to be overestimated in size and larger particles to be underestimated, though this did not have a statistically significant impact on the PSFD. This should be further explored for missions that require high particle measurement accuracy.

For the OSIRIS-REx mission, particle mapping was pivotal to spacecraft safety. The use of a GIS environment enabled us to tie particle measurements to real coordinates on Bennu, which enabled the identification of candidate sample sites and helped the spacecraft to avoid large particle hazards during sample collection.

On 20 October 2020, OSIRIS-REx successfully contacted the surface of Bennu at the Nightingale sample site [START_REF] Lauretta | Overcoming Challenges to Collect a Sample of the Early Solar System[END_REF]. Image analysis and event reconstructions suggest that more than 60 g of material were collected from the asteroid. The successful sample collection event on an asteroid with very limited unobstructed sampleable material at the surface underscores the value of using PSFDs to incrementally estimate the frequency of particles of a given size.

Figure 1 .

 1 Figure 1. Close-up examples of images of Bennu's surface with and without mapped particles.This example falls within the Nightingale region. Illumination conditions and pixel resolution are included for context. We define incidence as the angle between the light vector and the surface normal (Sun-Bennu-surface normal), emission as the angle between the observation vector and the surface normal (OCAMS-Bennu-surface normal), and phase as the angle between the light vector and observation vector (Sun-Bennu-OCAMS).

Figure 2 .

 2 Figure 2. Compilation of mapped particles in each mission phase. (a). Global counts re-produced from DellaGiustina and Emery et al. [24] with the four candidate sample sites are shown. (b). Change in the region of interest (ROI) size and location per imaging campaign is plotted on Baseball Diamond (BBD) images used for particle mapping for each of the four candidate sample sites. (c). Particles mapped during the BBD imaging campaign for each of the four candidate sample sites. (d). Particles mapped during the Recon A imaging campaign for each of the four candidate sample sites. (e). Particles mapped during the Recon C imaging campaign for each of the four candidate sample sites. The panels on the far right of (c-e) show close-ups of the counts made for Nightingale.

Figure 3 .

 3 Figure 3. Rock Tray 1 from the OSIRIS-REx particle measurement uncertainty analysis with remotely measured counts overlaid. Counts were performed in the same ArcMap mapping environment used for mission operations. Counters who mapped in ArcMap mapped the full image, but ground-truth caliper measurements were only collected for 85 of these rocks (shown in light blue).

Figure 4 .

 4 Figure 4. (a). Percent error between remotely sensed and ground-truth measurements. (b). Correlation plot between caliper measurements and remotely sensed measurements. Both panels demonstrate the slight trend of overestimating the measurement of small particles and underestimating the measurement of large particles. Vertical error bars represent the uncertainty in the remote measurements amongst all of the counters. Horizontal error bars represent the uncertainty in the caliper measurements.

Figure 5 .

 5 Figure 5. Cumulative PSFDs of caliper measurements and remotely sensed measurements. Light gray points indicate particle measurements that were smaller than the completeness limit. Error bars represent Poisson detection distribution uncertainty (square root of N C ).

Figure 7 .

 7 Figure 7. Differential PSFDs of Bennu for the four candidate sample sites as calculated at several key mission phases. Recon C mapping was only performed for the primary and back-up sample sites, Nightingale and Osprey. The global PSFD calculated from early OSIRIS-REx images of Bennu by DellaGiustina and Emery et al.[START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] is included as a reference. Light gray points indicate particle measurements that were smaller than the completeness limit.

Figure 8 .

 8 Figure 8. Relative PSFDs of Bennu for the four candidate sample sites as calculated at several key mission phases. Recon C mapping was only performed for the primary and back-up sample sites, Nightingale and Osprey. The global PSFD calculated from early OSIRIS-REx images of Bennu by DellaGiustina and Emery et al.[START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] is included as a reference. Light gray points indicate particle measurements that were smaller than the completeness limit.

Figure 9 .

 9 Figure 9. Cumulative PSFDs of Bennu using merged measurements based on the four key mission phases. The global PSFD calculated from early OSIRIS-REx images of Bennu by DellaGiustina and Emery et al.[START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] is included as a reference. Light gray points indicate particle measurements that were smaller than the completeness limit.

Figure 10 .

 10 Figure 10. Cumulative PSFD of Bennu based on measurements merged into a single dataset. Light gray points indicate particle measurements that were smaller than the completeness limit.

Figure 11 .

 11 Figure 11.Close-ups of the four candidate sample sites from a global normal albedo map of Bennu[START_REF] Hirata | Secondary craters of Tycho: Size-frequency distributions and estimated fragment size-velocity relationships[END_REF] showing that both comparatively bright and dark materials are present. ROIs shown (blue circles) are from Recon A.

Figure 12 .

 12 Figure 12. Cumulative surface coverage of PSFDs of Bennu using merged measurements based on the four key mission phases. The global PSFD calculated from early OSIRIS-REx images of Bennu by DellaGiustina and Emery et al.[START_REF] Dellagiustina | Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis[END_REF] is included as a reference. Light gray points indicate particle measurements that were smaller than the completeness limit. The black line denotes where 50% surface coverage is achieved.

Figure 13 .

 13 Figure 13. Cumulative surface coverage of PSFD of Bennu based on measurements merged into a single dataset. Light gray points indicate particle measurements that were smaller than the completeness limit. The black line denotes where 50% surface coverage is achieved.

Figure 14 .

 14 Figure 14. Close-ups of Nightingale (left) and Osprey (right) highlighting regions densely packed with counted particles. Nightingale has a larger proportion of sampleable particles (≤2.0 cm) than Osprey, which appears to be saturated with particles ~10.0 cm and larger.

Figure 15 .

 15 Figure 15. Same plot as Figure 10, but with a Weibull fit (displayed as black dashed line).

the

  Université Côte d'Azur. C.M. Elder, J.L. Molaro, and M. Pajola were supported by the OSIRIS-REx Participating Scientist Program. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable.

  Cumulative PSFDs of Bennu for the four candidate sample sites as calculated at several key mission phases. Recon C mapping was only performed for the primary and back-up sample sites, Nightingale and Osprey. The global PSFD calculated from early OSIRIS-REx images of Bennu by DellaGiustina and Emery et al.

		Mission Phase	Center Latitude/ Longitude	ROI Radius (m)	Surface Area Counted (m 2 )	Total Particles Counted	Min. Particle Length (m)	Max. Particle Length (m)	Est. CompletenessLimit (m)	Est. Power Law Index
	Global	Approach	[-70, +70], [0, 360]	N/A	663,000	3136	1.30	58.38	8.12 ± 1.59	-2.9 ± 0.3
		BBD	55.13, 42.41	10.00	314.14	556	0.05	1.96	0.25 ± 0.07	-1.9 ± 0.3
	Nightingale	Recon A	55.81, 42.20	13.10	417.75	17,867	0.01	4.71	0.15 ± 0.02	-2.3 ± 0.1
		Recon C	56.05, 42.05	4.24	61.74	26,171	0.004	1.51	0.05 ± 0.02	-2.2 ± 0.1
		BBD	11.55, 89.23	5.00	78.49	269	0.05	3.32	0.19 ± 0.05	-2.1 ± 0.4
	Osprey	Recon A	11.54, 88.58	8.50	242.50	11,013	0.02	5.83	0.25 ± 0.03	-3.0 ± 0.2
		Recon C	11.62, 88.63	3.02	33.27	28,929	0.003	0.70	0.11 ± 0.04	-2.7 ± 0.6
	Sandpiper	BBD Recon A	-47.17, 321.31 -46.98, 321.34	5.00 8.75	78.49 199.01	487 9059	0.07 0.01	1.42 2.14	0.32 ± 0.05 0.27 ± 0.05	-3.3 ± 0.4 -2.6 ± 0.2
	Kingfisher	BBD Recon A	11.41, 55.59 11.49, 55.49	5.00 7.75	78.49 146.02	547 5111	0.05 0.02	1.90 2.35	0.19 ± 0.05 0.22 ± 0.02	-2.1 ± 0.2 -2.5 ± 0.1
			Figure 6.

Acknowledgments: This research made use of the U.S. Geological Survey's (USGS) Integrated Soft-

Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). We are grateful to the entire OSIRIS-REx Team for making the encounter with Bennu possible. K.

Data Availability Statement: OCAMS images used for particle counting are available via the Planetary Data System (PDS) [START_REF] Rizk | Spectral Interpretation, Resource Identification, Security, Regolith Explorer (OSIRIS-REx): OSIRIS-REx Camera Suite (OCAMS) Bundle. NASA Planetary Data System[END_REF]. Data are delivered to the PDS according to the OSIRIS-REx Data Management Plan available in the OSIRIS-REx PDS archive [START_REF] Crombie | Spectral Interpretation, Resource Identification, Security, Regolith Explorer (OSIRIS-REx): Mission Bundle. NASA Planetary Data System[END_REF]. Shape models of Bennu are available via the Small Body Mapping Tool at http://sbmt.jhuapl.edu/ (accessed on 26 March 2021). The particle measurement data are available upon request (knburke@email.arizona.edu).