Agostino Martinelli

Adriana Tapus

Kai Olivier Arras

Roland Siegwart

Multi-resolution SLAM for Real World Navigation

In this paper a hierarchical multi-resolution approach allowing for high precision and distinctiveness is presented. The method combines topological and metric paradigm. The metric approach, based on the Kalman Filter, uses a new concept to avoid the problem of the drift in odometry. For the topological framework the fingerprint sequence approach is used. During the construction of the topological map, a communication between the two paradigms is established. The fingerprint used for topological navigation enables also the re-initialization of the metric localization. The experimentation section will validate the multi-resolution-representation maps approach and presents different steps of the method.

Introduction

Many methods have been proposed to represent an environment in the framework of autonomous navigation, from precise geometric maps based on raw data or lines up to purely topological maps using symbolic descriptions. Each of these methods is optimal concerning some characteristics but can be very disappointing with respect to other requirements. In particular, none of them is able to cope with the large variety of environments that humans encounter in their daily live.

Hierarchical Multi-Resolution maps

Most current approaches make a trade-off between precision and global distinctiveness. Precision and distinctiveness have a strong link with the level of abstraction of the features used for navigation (fig. 1). Raw data represent the lowest level in the hierarchy of abstraction. Localization and mapping with raw data can result in very high precision of the represented environment, but the required data volume scales very badly with the size of the environment and the distinctiveness of the individual data points is very low. An example of such a approach is Markov localization [START_REF] Fox | Markov Localization: A Probabilistic Framework for Mobile Robot Localization and Navigation[END_REF][START_REF] Thrun | Robust Monte Carlo Localization for Mobile Robots[END_REF]. The second level of abstraction corresponds to the geometric features (lines, edges). The stochastic map technique to SLAM [START_REF] Castellanos | Mobile Robot Localization and Map Building: Multisensor Fusion Approach[END_REF][START_REF] Dissanayake | A Solution to the Simultaneous Localization and Map Building (SLAM) problem[END_REF][START_REF] Leonard | Directed Sonar Sensing for Mobile Robot Navigation[END_REF] and the multi-hypothesis localization [START_REF] Arras | Feature-based multihypothesis localization and tracking using geometric constraints[END_REF] are typical examples belonging to this level. These approaches still feature high precision with reduced memory requirements, but have shortcomings concerning global distinctiveness and unmodeled events. Partially geometric features correspond to the third level of the hierarchy. Representations using partially geometric features are for examples fingerprints (a sequence of low level features) described in [START_REF] Lamon | Deriving and Matching Image Fingerprint Sequences for Mobile Robot Localization[END_REF][START_REF] Lamon | Environmental Modeling with Fingerprint Sequences for Topological Global Localization[END_REF], but also more bio-inspired approaches [START_REF] Arleo | Spatial Cognition and Neuro-Mimetic Navigation: a model of Hippocampal Place Cell Activity[END_REF][START_REF] Berthoz | Le sens du mouvement[END_REF][START_REF] Hafner | Learning Places in Newly Explored Environments[END_REF] using neural networks, e.g. the work by Hafner [START_REF] Hafner | Learning Places in Newly Explored Environments[END_REF] uses a neural network to create a topological map of the environment based on images of an omni-directional camera. On the highest abstraction level the environment is represented by a symbolic description. This can be very compact and distinctive, but reliable tools for extraction of high level features are still missing. The aim of the present work is to suggest and discuss a multilevel representation approach for robust and compact environment representation. This is realized by integrating different level of abstraction and representations in a common navigation framework. For example, to get from the airport to a given room in a hotel, maps of the city streets and of the hotel are necessary. Clearly, these maps are on different scales and different representations (e.g. metric/topological). A crucial point is then the linkage between two maps of different resolution. In the multi-level representation we propose, the mobile robot uses the most suitable level of abstraction, depending on the task it has to accomplish and the certainty about its pose. Moreover, depending on the actual situation, it has to be able to switch from one level to another one (see figure 1).

In this paper we will discuss the possibility to integrate most recent results in mobile robot navigation in a multi-level hierarchical representation and we will present our first attempts towards multi-resolution, multi-representation maps.

2

First attempt for a multi-resolution Map

Metric Mapping based on a Relative Map Filter

In this section we introduce a new approach to solve the SLAM problem in the framework of the stochastic map based on the concept of the relative map. The aim of this method is to minimize the loop consistency problem (i.e. the global convergence and consistency of the built map in large environment -large meaning when the size of the environment is much larger than the range of the adopted external sensor). Clearly, even with this approach the problem of the consistency of the built map cannot be completely solved and therefore, for very large environment, it is necessary to combine the metric approach with a topological approach (see the next sections) and several local maps give the global metric description. However, the relative map introduced here increases the convergence properties of the map with respect to the standard approach since the convergence of the map built following the standard approach [START_REF] Dissanayake | A Solution to the Simultaneous Localization and Map Building (SLAM) problem[END_REF] requires infeasible hypothesis (odometry perfectly modelled and linearity of the observation in the estimated state (see [START_REF] Dissanayake | A Solution to the Simultaneous Localization and Map Building (SLAM) problem[END_REF] for details)).

The basic idea consists of introducing a map state, which only contains quantities invariant under translations and rotations. This is the only way in order to have an actual decoupling between the robot and the landmark estimation and therefore to do not rely the landmark estimation on the unmodeled error sources in the robot motion. Once a relative map is estimated and the absolute location of a set of landmarks is known (e.g. by using the first observation) it is possible to build the absolute map. Therefore, the entire method contains two algorithms. The former estimates the relative map, the latter builds the absolute map. Only the case of point landmark is here considered, although the same idea could be applied to other kind of landmark. In the sections 2.1.1 and 2.1.2 respectively we describe the two algorithms.

The Relative Map Filter

The state estimated through this filter only contains the distances between the point landmarks. Clearly, the distance is a quantity invariant under translation and rotation, i.e. it is independent of the robot configuration.

Let denote with d the state and with P its covariance matrix. In Fig 2a the vector d contains the marked distances between the 6 landmarks. Clearly, not all of the distances between the 6 landmarks are stored in d because not all the landmarks were observed together at the same time. At a given time step, the observation consists of a set of distances between the landmarks observed by the robot through its external sensor (Fig 2b). Clearly, these distances may be already observed (i.e. can be in the vector d) or may not. Let introduce the following notation:

d old =[u, w old ] T d obs =[w obs , v] T (1)
where d old is the state estimated at a given time step and d obs is the observation at the same time step, containing a set of distances between the landmarks observed by the robot. u contains the distances which are not re-observed (i.e. which do not appear in the vector d obs ) and w old contains the distances re-observed (denoted by w obs in the vector d obs ). Finally, v , contains the distances observed for the first time at the considered time step. The covariance matrix of the previous vectors are:

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ = ww T uw uw uu old P P P P P ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ = vv T wv wv ww obs R R R R P (2)
We adopt the following notation to denote the estimated quantities, obtained by fusing the old state with the observed one (the new estimated distances are depicted in Fig2c).

d new =[u new , w new, v new ] T (3)
We obtain the new estimation for the state and its covariance matrix by applying the equations of the Kalman filter.

u new = u + P uw (P ww + R ww ) -1 (w obs -w old ) (5) w new = w old + P ww (P ww + R ww ) -1 (w obs -w old ) (6) v new = v + R vw (P ww + R ww ) -1 (w old -w obs ) (7) Pn uu = P uu -P uw (P ww + R ww ) -1 P wu (8) Pn uw = P uw -P uw (P ww + R ww ) -1 P ww (9) Pn uv = 0 (10) Pn ww = P ww -P ww (P ww + R ww ) -1 P ww [START_REF] Kanade | Stereo by Intra-and Inter-Scanline Search Using Dynamic Programming[END_REF]

Pn wv = R wv -R ww (P ww + R ww ) -1 R wv (12) Pn vv = R vv -R vw (P ww + R ww ) -1 R wv (13)

Recovering the Absolute Landmark Location

We adopt a simple linear method to recover the absolute landmark locations starting from the absolute location of three or more landmarks and the state estimated by the previous filter, which contains the distances between the landmarks. At a given time step the absolute locations of a set of landmarks are available (we assumed that the absolute coordinates of at least three landmarks are known at the beginning; these coordinates could be provided by the first observation). The aim is to estimate the location of a new landmark denoted by j.

We extract from the previous set a subset containing the landmarks whose distance from the landmark j is provided by the relative filter. Let denote the locations of these landmarks by (x i , y i ) and the distance between the landmark j and the landmark i of this subset by d i . We assumed that the number of the elements of this subset is equal to n. If n<3 the absolute location of the landmark j cannot be provided. Clearly, we have for the landmark i

⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = vv
d i 2 = (x j -x i ) 2 +(y j -y i ) 2 (14)
We therefore obtain a linear system in the unknowns x j and y j by considering all the differences d i 2 -d 1 2 . By applying recursively this method for all the landmarks (all j) it is possible to get their absolute location

Topological Map

The topological approach tries to give a compact representation since only distinctive places within the environment are encoded. One of the main problems of this method is the perceptual aliasing (i.e. distinct locations within the environment appearing identical to the robot's sensors). In order to be capable to eliminate the perceptual aliasing problem, the distinctiveness of the space must be improved. To maximize the reliability in navigation, the information from all the sensors that are available to the robot must be used. To solve this problem the notion of fingerprint as described in [START_REF] Lamon | Deriving and Matching Image Fingerprint Sequences for Mobile Robot Localization[END_REF][START_REF] Lamon | Environmental Modeling with Fingerprint Sequences for Topological Global Localization[END_REF] is used. This characterization of the environment is especially interesting when used within a topological localization and multiple modalities framework. A fingerprint is a circular list of features, where the ordering of the set matches the relative ordering of the features around the robot. We denote the fingerprint sequence using a list of characters, where each character represents the instance of a specific feature type. In our case we choose to extract color patches and vertical edges from visual information and corners and beacons from laser scanner. We decided to use the letter 'v' to characterize an edge, the letters A,B,C,...,P to represent hue bins, the letter 'c' to characterize a corner feature and the letter 'b' to characterize a beacon feature. Details about the visual features extraction can be found in [START_REF] Lamon | Environmental Modeling with Fingerprint Sequences for Topological Global Localization[END_REF] and laser scanner features extraction can be found in [START_REF] Arras | Feature Extraction and Scene Interpretation for Map-Based Navigation and Map Building[END_REF].

Fingerprints matching for localization

The string-matching problem is not an easy one. Usually strings don't match exactly because the robot may not be exactly located on a map point and/or some changes in the environment or perception errors occurred. The standard algorithms are quite sensitive to insertion and deletion errors, which cause the string lengths to vary significantly.

Minimum energy algorithm

The approach adopted for sequence matching is inspired by the minimum energy algorithm used in stereo-vision for finding pixels in two images that correspond to the same point of a scene [START_REF] Kanade | Stereo by Intra-and Inter-Scanline Search Using Dynamic Programming[END_REF]. As in the minimum energy case, the problem can be seen as an optimization problem, where the goal is to find the path that spends the minimum energy to go from the beginning to the end of the first sequence considering the values of the second one. The similarity between two sequences is given by the resulting minimum energy of traversal.

Fingerprint generation

The fingerprint generation is done in three steps (see Fig. 3). The first step consists in extracting the different features from the panoramic image and the laser scan: vertical edges, patches of colors, corners and beacons. The features are arranged in an array along with their corresponding position (from 0 to 359 degrees). At this stage a new type of feature that reflects a correspondence between a corner and an edge: the feature 'f', is introduced, more details can be found in [START_REF] Lamon | Environmental Modeling with Fingerprint Sequences for Topological Global Localization[END_REF]. The ordering of the features in a fingerprint sequence is highly informative and for that reason the notion of angular distance between two consecutive features will be added. This adds geometric information and increases once again the distinctiveness between the fingerprints. Therefore, we decided to introduce a new type of feature, the empty space feature 'n', for reflecting angular distance. Each 'n' covers the same angle of the scene (20 degrees). So, as many empty spaces as needed must be inserted in order to fill the gap between two consecutive features. This insertion is the last step of the fingerprint generation. By regrouping all this results together and by adding the empty space features, the final fingerprint is: cbccbnfGcnEnvccncbcvncnnfvvvnccAcb

Multi-resolution Map

Our approach combines low-level feature for local metric and fingerprints for global topological localization and mapping. Indeed, the combination of these two levels of abstraction is necessary, because the consistency in large environments with stochastic maps is impossible. The relative map approach described in Section 2.1 increases the convergence property. The estimation does not rely on the odometry and therefore on the unmodeled events in the robot motion. However, this method fails when the unmodeled events (e.g. strong collision) are strong enough to cause error in data association. Clearly, the stochastic maps completely fail when there is a kidnapping during the motion.

The main problem that arises when there are several levels of abstraction is the switching between the levels. In our case, this appears when we switch from topological to metric. In order to deal with the switching problem, we introduce a new element in the fingerprint approach. The new fingerprint contains the fingerprint as illustrated in Section 2.2, and the local coordinates of the correspondent beacons as appearing in the local metric map. To enable the generation of this new fingerprint, a communication between the two levels of abstraction is required.

When a kidnapping is performed, in order to find the new location of the robot, the fingerprint approach will be used. Once the location is found, the association between the local coordinates of the beacons (contained in the matched fingerprint) and the observed fingerprint is done. In this way the re-initialization of the metric navigation is accomplished. This multi-representation approach enables SLAM on two levels of abstraction, thus featuring precision and global consistency. A similar concept can be found in [START_REF] Tomatis | Hybrid Simultaneous Localization and Map Building: Closing the Loop with Multi-Hypotheses Tracking[END_REF].

Experimental Results

For the experiments, Donald Duck (see Fig. 4a), a fully autonomous mobile robot, has been used. The robot is equipped with wheel encoders, a 360° laser range finder and an omnidirectional camera. The panoramic vision system depicted in figure 4b uses a mirror-camera system to image 360° in azimuth and up to 110° in elevation. The use of an omnidirectional camera combines the advantages of the SICK laser range finder (e.g. an angle of view of 360°) and the capability of detecting verticals. Twenty-two beacons were placed in the environment. They could be detected by the laser sensor with an accuracy of around 5 cm. There were adopted to create the point landmarks mentioned in section 2. Clearly, instead of them a function able to extract corners from laser scanner could be used.

Metric Map

Figure 5 shows the metric map obtained through the relative map filter described in the section 2.1.1. The robot visited three rooms and estimated at each time step its configuration and the positions of the 22 beacons in the environment. Since the odometry was completely decoupled by the estimation process (as explained in the section 2.1) there is not any drift in the built map and in particular it was possible to adopt a unique global metric map. During the experiment the odometry data were only used to solve the data association problem and not in the estimation process. The initial robot configuration coincides with the origin of the global reference whose axis were chosen coincident with the axis of the robot at the initial time. The grey line shows the robot trajectory computed by using the same algorithm described in the section 2.1.1 and the symbol 'O' is adopted to indicate the absolute beacon position.

Topological map

In order to validate the fingerprint approach, for each of the four rooms (see Figure 5), a fingerprint has been extracted. This experiment has been repeated six times for each room, and the fingerprint has been extracted in different locations of the room. Three fingerprints per room have been included in a database as reference (map). The others 12 fingerprints (3 per room) have been matched to the database for testing the localization. For a given observation (fingerprint), a match is successful if the best match with the database (highest probability) corresponds to the correct room. For our experiments the match was successful for all the test fingerprints and the correct room has always been found with the highest probability, a probability going from 0.67 to 0.92. Kidnapping and metric re-initialization Three kidnapping were performed, respectively in Room1, Room2 and Room4 (see figure 5). In the Table 1 the results of the matching algorithm presented in Section 2.2.1, are normalized to have a probability (between 0 and 1). As it can be seen the correspondence between the real location and the observed one is always found with a high probability.

Concerning the metric re-initialization, the results are showed in the figure 5, and the estimated robot positions are indicated with symbol '*'.

The error between the metric position that have been found and the real position of the robot is very small, the error going from 1 to 4 cm.

Conclusion and Outlook

This paper presented a multi-level hierarchical representation. The new approach depicted combines metric and topological concept. The two paradigms are on two different levels of abstraction. This kind of representation allows a very compact and computationally efficient representation of the environment for mobile robot navigation. The results of our first attempts towards multi-resolution maps showed the robustness of the approach. Future works will focus on experiments in large environments, on the introduction of an average fingerprint instead of several fingerprints for each node, on a probabilistic fingerprint-matching concept, on an automatic generation of nodes and on the extension of the relative map filter to line landmark.

Fig. 1 .

 1 Fig. 1. This figure depicts the hierarchy of abstraction levels. More we go up in the hierarchy, more we reduce the geometric information and more we increase the distinctiveness. For global localization and mapping, high distinctiveness is of importance, whereas for local action, precise geometric relations with the environment come forward.

Fig. 2 .

 2 Fig. 2. Relative Map before the observation (a), the observation (b), and the relative map obtained by fusing the information coming from the old map and the observation (c). In all the three figures the map state only contains the indicated distances between the landmarks

Fig. 3 .

 3 Fig. 3. Fingerprint generation. (a) panoramic image with the vertical edges and color patches detection 'v' and color (b) laser scan with extracted corners 'c' and beacons 'b' (c) the first three images depict the position (0 to 360°) of the vertical edges, the corners, the beacons and the colors (G-green, E-light green, and A-red) respectively. The fifth image describes the correspondence between the vertical edges features and the corner features. By regrouping all this results together and by adding the empty space features, the final fingerprint is: cbccbnfGcnEnvccncbcvncnnfvvvnccAcb

Fig. 4 .

 4 System used for experimentation: a) The fully autonomous robot Donald Duck. b) The panoramic vision system. The camera has a 640x480 pixels resolution and an equiangular mirror is used so that each pixel in the image covers the same view angle

Fig. 5 .

 5 Fig. 5. Local map of the environment with the way traversed by the robot, with the numeroted seen beacons and with the estimated metric position '*'

Table 1 .

 1 Probabilities for matches between the database fingerprints and the observed

	fingerprints
	Fingerprint	Room1	Room2 Room4
	Room1_1	0.72	0.37	0.50
	Room1_2	0.57	0.64	0.39
	Room1_3	0.61	0.66	0.44
	Room2_1	0.51	0.69	0.38
	Room2_2	0.49	0.92	0.48
	Room2_3	0.39	0.82	0.49
	Room4_1	0.42	0.48	0.65
	Room4_2	0.56	0.32	0.79
	Room4_3	0.49	0.58	0.55


Lu Xie

Pascal Brault
email: pascal.brault@univ-orleans.fr

Christophe Coutanceau

Jean-Marc Bauchire

Amael Caillard

Steve Baranton

Johannes Berndt

Erik C Neyts

Efficient amorphous platinum catalyst cluster growth on porous carbon: A combined Molecular Dynamics and experimental study

Keywords: Molecular dynamics, plasma sputtering deposition, cluster growth, Pt catalyst, fuel cell electrodes

Amorphous platinum clusters supported on porous carbon have been envisaged for high-performance fuel cell electrodes. For this application, it is crucial to control the morphology of the Pt layer and the Ptsubstrate interaction to maximize activity and stability.

We thus investigate the morphology evolution during Pt cluster growth on a porous carbon substrate employing atomic scale molecular dynamics simulations. The simulations are based on the Pt-C interaction potential using parameters derived from Density Functional Theory and are found to yield a Pt cluster morphology similar to that observed in low loaded fuel cell electrodes prepared by plasma sputtering. Moreover, the simulations show amorphous Pt cluster growth in agreement with X-ray diffraction and Transmisson Electron Microscopy experiments on high performance low Pt content (10µg Pt cm -2 ) loaded fuel cell electrodes and provide a fundamental insight in the cluster growth mechanism.

Introduction

Physical and electronic properties of metal clusters deposited on various substrates have recently received a great deal of attention. Noble metal clusters, particularly Ru, Rh, Pd, Pt and Au, [START_REF] Muroi | Role of Precious Metal Catalysts[END_REF] are very often used in catalytic reactions. [START_REF] Chen | Platinum-Based Nanostructured Materials: Synthesis, Properties, and Applications[END_REF][START_REF] Selvaraj | Synthesis and characterization of metal clustersdecorated PPY-CNT composite and their electrocatalytic oxidation of formic acid and formaldehyde for fuel cell applications[END_REF] In heterogeneous catalysis, reactions occur at the catalyst surface, so that a high surface-to-volume ratio leading to a large fraction of accessible atoms is required for increasing the activity of the catalyst [START_REF] Narayanan | Changing Catalytic Activity During Colloidal Platinum Nanocatalysis Due to Shape Changes: Electron Transfer Reaction[END_REF][START_REF] Hashmi | The First Gold-Catalyzed C-S Bond Formation: Cycloisomerization of α-Thioallenes to 2,5-Dihydrothiophenes[END_REF][START_REF] Xiong | Nanocrystals with Unconventional Shapes -A Class of Promising Catalysts[END_REF] , and for decreasing its cost. There is thus a real interest to obtain the highest catalytic surface area from a low metal weight. Currently, a very important application of noble metals is their use for activating electrochemical reactions occurring in proton exchange membrane fuel cells (PEMFCs), [START_REF] Gupta | Carbon-supported platinum catalysts for direct alcohol fuel cell anode[END_REF][START_REF] Li | Carbon nanotubes as support for cathode catalyst of a direct methanol fuel cell[END_REF][START_REF] Joo | Ordered nanoporous arrays of carbon supporting high dispersions of platinum clusters[END_REF] such as the sluggish oxygen reduction reaction. [START_REF] Ralph | Platinum Metal Rev. Catalysis for Low Temperature Fuel Cells, Part I: The Cathode Challenges[END_REF][START_REF] Stamenkovic | Improved Oxygen Reduction Activity on Pt 3 Ni(111) via Increased Surface Site Availability[END_REF] In this latter case, Ptbased clusters are supported by nanostructured carbon substrates, among them disordered porous carbon structures [START_REF] Gasteiger | Activity benchmarks and requirements for Pt, Pt-alloy, and non-Pt oxygen reduction catalysts for PEMFCs[END_REF][START_REF] Chan | Supported mixed metal clusters as electrocatalysts in low temperature fuel cells[END_REF] and ordered carbon structures, such as nanotubes (CNTs)/carbon nanofibers (CNFs). [START_REF] Che | Carbon nanotubule membranes for electrochemical energy storage and production[END_REF][START_REF] Tian | Highly Order -Structured Membrane Electrode Assembly with Vertically Aligned Carbon Nanotubes for Ultra-Low Pt Loading PEM Fuel Cells[END_REF] Lee et al. reported on the Pt cluster size distribution as a function of Pt loading for electrodeposited Pt nanocrystal on highly orientated pyrolytic graphite (HOPG) surfaces and demonstrated that the average cluster size increased as the Pt loading increased, [START_REF] Lee | Growth of electrodeposited platinum nanocrystals studied by atomic force microscopy[END_REF] resulting in the decrease of the active surface area. Several methods were proposed for lowering the Pt loading: by alloying Pt with foreign metal atoms, [START_REF] Stamenkovic | Trends in electrocatalysis on extended and nanoscale Pt-bimetallic alloy surfaces[END_REF][START_REF] Hwang | Role of electronic perturbation in stability and activity of Pt-based alloy nanocatalysts for oxygen reduction[END_REF] by forming Pt-based core-shell structures, [START_REF] Zhang | Controlling the Catalytic Activity of Platinum-Monolayer Electrocatalysts for Oxygen Reduction with Different Substrates[END_REF][START_REF] Zhang | Design of Pt-Shell Clusters with Alloy Cores for the Oxygen Reduction Reaction[END_REF] , by localizing the catalytic particle close to the proton conductive solid electrolyte, [START_REF] Cavarroc | Performance of plasma sputtered Fuel Cell electrodes with ultra-low Pt loadings[END_REF] by modifying Pt cluster surface with a proton conductive polymer, [START_REF] Ferrandez | Pt Particles Functionalized on the Molecular Level as New Nanocomposite Materials for Electrocatalysis[END_REF][START_REF] Ferrandez | Chemical Functionalization of Carbon Supported Metal Clusters by Ionic Conductive Polymer via the "Grafting From[END_REF] etc.

One of the major degradation factors of the electrical performances of PEMFC electrodes however is the agglomeration process of metal clusters under fuel cell working conditions, [START_REF] Sellin | Effects of Temperature and Atmosphere on Carbon-Supported Platinum Fuel Cell Catalysts[END_REF][START_REF] Dubau | An identical-location transmission electron microscopy study on the degradation of Pt/C clusters under oxidizing, reducing and neutral atmosphere[END_REF] due to their mobility on the carbon supports. [START_REF] Urchaga | Improvement of the platinum clusterscarbon substrate interaction by insertion of a thiophenol molecular bridge[END_REF] It is then necessary to keep the Pt clusters well attached to and dispersed on the nanostructured carbon support to avoid their agglomeration over time, which would lead to the loss of surface area and mass activity. [START_REF] Tseung | Loss of surface area by platinum and supported platinum black electrocatalyst[END_REF] However, Clark and Kesmodel [START_REF] Clark | Ultrahigh vacuum scanning tunneling microscopy studies of platinum on graphite[END_REF] studied very small Pt clusters in the order of a few nm and demonstrated that their migration over the nanoporous surface leads to coalescence which in turn leads to the formation of a more stable and larger cluster.

Accordingly, Lee et al. [START_REF] Lee | Growth of electrodeposited platinum nanocrystals studied by atomic force microscopy[END_REF] reported that the diameter distribution of mobile Pt clusters have a maximum around 14 nm. The morphology, microstructure and interaction with the support of the metal clusters are therefore properties recognized as driving the activity and stability of the catalyst. Many efforts are then directed at optimizing the catalytic performance, which in turn requires a thorough understanding of both the relationship between the nanocatalyst deposition process and the nanocatalyst activity, as well as the Ptsubstrate interactions [29,30] .

The ability to predict -and ultimatelydesign stable and highly active Pt clusters supported on a porous carbon substrate is thus of paramount importance. Classical reactive molecular dynamics (MD) simulations was used to investigate the dynamical and structural evolution of platinum cluster growth on a nanostructured porous carbon substrate at the atomic scale by a plasma sputtering method. Such metal deposition method has proven to be very efficient for the preparation of highly active low Pt loaded PEMFC electrodes. [START_REF] Hirano | High performance proton exchange membrane fuel cells with sputter-deposited Pt layer electrodes[END_REF][START_REF] Haug | Increasing Proton Exchange Membrane Fuel Cell Catalyst Effectiveness Through Sputter Deposition[END_REF][START_REF] Brault | Plasma sputtering deposition of platinum into porous fuel cell electrodes[END_REF] We will demonstrate how these atomic scale simulations provide insight in the influence of the deposition conditions on the cluster growth and the resulting Pt morphology. Finally, we develop a plasma method for preparing Pt cluster deposited on carbon and provide a comparison between our simulation results and experimental results on the structural and morphological evolution of the Pt-clusters during the growth, which are leading to high performance fuel cell electrodes.

Experimental

The deposition chamber is equipped with two rectangular targets: one of pure carbon and one of Pt 0.01 C 0.99 . Deposition conditions are as follows: power 530 W, target voltage 700 V, and target current 0.78 A. The growth rate is 4 nm.min -1 . The target-to-substrate distance is 6.5 cm.

Targets are 45° tilted with respect to the substrate. Conventional uncatalyzed E-Tek carbon porous layers (CPL) on a carbon woven web are used as substrates. Electrodes are loaded at 0.010 mg cm -2 Pt . The Pt loading and localization profile inside the CPL was determined by performing Rutherford backscattering spectroscopy: 90% of Pt atoms were localized in the first 200 nm depth of the material.

TEM images were obtained using a JEOL JEM 2010 (equipped with a LaB6 filament and with a resolution of 0.35 nm). The size distribution was estimated from the determination of the diameter from 100 particles using ImageJ free software [34] .

The XRD measurements were performed on a Bruker D 5005 Bragg-Brentano diffractometer operated with a copper tube powered at 40 kV and 40 mA (CuK 1 =1.5406 Å) with 0.06° step and a fixed acquisition time of 10 s/step. The catalytic powder scraped from a catalyzed CPL was deposited on a Kanthal foil and measurements were carried out in the 2θ range from 20° to 60°. The acquisition of the whole pattern was performed for 183 s at room temperature.

The instrumental resolution function of the diffractometer was evaluated from the pattern (10-155.5°) of the NIST SRM 660 (LaB 6 ) line profile standard. XPS measurements were performed by using an Escalab MKII (VG scientific) set-up using the magnesium monochromatic beam (1253.6 eV) at room temperature at pressures below 8•10 -9 Torr in the analysis chamber. Core level spectra were recorded at a 50 meV resolution. Binding energies were lined up with respect to the C1s peak at 284.6 eV.

The Membrane electrode assembly for fuel cell tests consisted in two 0.010 mg Pt cm -2 Pt/CPL electrodes with 5 cm 2 surface area mechanically pressed on a Nafion 212 membrane at 2 Nm torque in the cell hardware (Electrochem). No preliminary hot pressing process of electrodes against the Nafion 212 membrane (used as received from Electrochem. Inc.) was performed.

No Nafion solution was added in the electrode catalytic layers before use. Under our testing conditions, the pressure is manually regulated with the output valves and hydrogen and oxygen are humidified by bubbling in water at 80°C and 40°C, respectively. Measurements in a 5 cm 2 PEMFC using pure H 2 and O 2 gases are performed using a ECL150/MTS 150/HSA unit (Electrochem. Inc.). The polarization curves are recorded by applying increasing current values to the cell and reading the voltage stabilization (at least 30 s stabilization time for each current value).

Molecular Dynamics Modeling

The MD simulations are intended to mimic the Pt-cluster growth process from Pt-atom deposition on a carbon nanoporous substrate. A realistic model for this substrate is constructed by applying a constrained reverse Monte-Carlo procedure designed to reproduce a set of high resolution transmission electron microscopy pictures. [START_REF] Pikunic | Structural modeling of porous carbons: constrained reverse Monte Carlo method[END_REF] The dimensions of the model substrate are 6 x 6 x 6 nm 3 , containing 17040 atoms, corresponding to a density of 1.57 g cm -3 and a porosity of 48%. Periodic boundaries are applied in the lateral directions, thus exposing the top of the structure as a free surface.

2500 platinum atoms are released towards the substrate every ∆t = 2 ps. The initial position of the Pt atom is 8 Å above the substrate and with randomly chosen {x,y} coordinates. Pt atoms interact with other Pt atoms and with the nanostructured carbon substrate atoms within a cutoff distance of 8 Å. The initial velocities of the incoming Pt atoms are sampled from a Maxwell-Boltzmann distribution with three most probable mean kinetic energies <E deposit > of 1 eV, 0.1 eV and 0.026 eV and with randomly chosen incident angles. The mean kinetic energy <E deposit > of the incoming atoms is calculated according to a modified Thompson formula for atoms travelling through a plasma [START_REF] Meyer | Thermalization of sputtered atoms[END_REF][START_REF] Gras-Marti | Slowing down and thermalization of sputtered particle fluxes: Energy distributions[END_REF] over a defined target-to-substrate distance.

In the case of a mean kinetic energy <E deposit > = 1 eV, the simulation corresponds to sputtering experiments at low argon pressure where a small amount of buffer gas only randomizes the sputtered atom velocities with little energy loss. The second case studied, <E deposit > = 0.1 eV, either corresponds to resistive or e-beam evaporation, which produces a vapour at the vaporization temperature of ca. 0.1 eV. Plasma sputtering deposition at a gas pressure around 2 Pa also produces a vapor with mean kinetic energy around 0.1 eV. In the last case, where <E deposit > = 0.026 eV, the simulation mimics a metal vapor at the temperature of 300 K which occurs when sputtered Pt atoms travel across an argon plasma at a pressure of around 5 Pa.

The temperature of the substrate in all simulations is assumed to be 300 K. The substrate temperature is controlled by applying a Berendsen heat bath, employing a relaxation time of 1.17 ps. The carbon-carbon interactions in the substrate are modeled by a Tersoff potential. [START_REF] Tersoff | Empirical interatomic potential for carbon, with applications to amorphous carbon[END_REF] The platinum-platinum interactions are modeled through an EAM potential. [START_REF] Daw | Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals[END_REF][START_REF] Foiles | Application of the embedded-atom method to liquid transition metals[END_REF][START_REF] Foiles | Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys[END_REF][START_REF] Daw | The embedded-atom method: a review of theory and applications[END_REF][START_REF] Foiles | Contributions of the embedded-atom method to materials science and engineering[END_REF] The platinum-carbon interactions are modeled using a 12-6 Lennard-Jones (LJ) potential. We used parameters that were derived by Morrow and Striolo, [START_REF] Morrow | Assessing how metal-carbon interactions affect the structure of supported platinum clusters[END_REF] based on DFT calculations by Acharya et al. [START_REF] Acharya | Characterizing the interaction of Pt and PtRu clusters with boron-doped, nitrogen-doped, and activated carbon: Density functional theory calculations and parameterization[END_REF] for the binding energy of Pt on various graphite sites. The DFT data was then used to generate a potential energy surface, to which the Lennard-Jones interaction potential was fitted. According to this parameterization, the characteristic Pt -C interaction length is σ PtC = 1.60 Å and energy, ε PtC = 0.1365 eV, which are significantly different from previous sets [START_REF] Liem | Simulation study of platinum adsorption on graphite using the Sutton-Chen potential[END_REF][START_REF] Liem | Effective pairwise potential for simulations of adsorbed platinum[END_REF][START_REF] Sutton | Long-range Finnis-Sinclair potentials[END_REF][START_REF] Graves | Molecular dynamics for low temperature plasma-surface interaction studies[END_REF] . Indeed, we have chosen to use this new parametrization, as the previously used sets gave rise to very weak substrate bonding and the formation of Pt clusters which are invariably crystalline, contrary to our experiments (see below).

Results and discussion

The condensation coefficient of Pt onto the porous substrate is 0.83±0.02 and does depend on the incoming kinetic energy.

Snapshots obtained from these simulations are shown in Figure 1, for the three impact energy distributions considered here. It can be seen in Figure 1 that simulations result in the formation of thin film-like structures for all kinetic energies investigated. The relatively higher binding energy allows the Pt deposition to closely wet the substrate morphology. Moreover, the Pt atoms are allowed to diffuse through the pores of the substrate, resulting in an overall smoother and flatter surface morphology. This result is in agreement with experimental plasma sputtering deposition of Pt on porous carbon, demonstrating the Pt diffusion into the porous carbon substrate. [START_REF] Caillard | Deposition and diffusion of platinum clusters in porous carbon assisted by plasma sputtering[END_REF][START_REF] Brault | Anomalous diffusion mediated by atom deposition into a porous substrate[END_REF][START_REF] Caillard | Improvement of the sputtered platinum utilization in proton exchange membrane fuel cells using plasma-based carbon nanofibers[END_REF] The Pt concentration profiles for the three set of kinetic energy distribution centered at 0.26, 0.1 and 1.0 eV are plotted in Figure 2. For these three sets of calculation the concentration profile exhibits a bell shape, as in the case for thermal diffusion. When increasing the incoming kinetic energy, the concentration profile is shifted towards the in-depth of the substrate. Radial distribution function (RDF) plots, counting the neighbors at a given distance, for the Pt deposits are shown in Figure 3 and detailed in Table 1. For the three kinetic energy distributions of the depositing Pt atoms investigated here, the RDF first peak is very broad.

Moreover, the third and fourth peaks are overlapping for all energies, while the second peak, corresponding to 2 nd neighbor distance expected in bulk crystalline Pt is missing. This is due to the fact that the Pt clusters are wetting the disordered surface, such that the parallel atomic planes below and above a Pt atom (where the 2nd neighbors are lying in a face centered cubic crystal), are not defined. Consequently, the corresponding peak does not appearing in the Table 1. RDF peak positions corresponding to Figure 3 of the deposited Pt structures grown on the porous carbon substrate displayed in Figure 2, and the comparison to the Pt bulk crystal values. To further resolve the the ordered/disordered state of the Pt deposits showin in Figure 1, we calculate their resulting X-ray ray diffraction (XRD) patterns. The calculated X-ray intensities vs. 2θ of the deposited Pt clusters are shown in Figure 4 and detailed in Table 2. It can be seen that only two broad peaks arise for each sample, which can be attributed to Pt(111) and Pt(220) orientations. This observation is consistent with some order in the plane of the surface and the fading of 2nd and other neighbor distances.

--- ---- ---- ---- Pt (0.1 eV) 40.73 ---- 72.8 ---- ---- ---- ---- Pt (0.026 eV) 40.69 ---- 74.6 ---- ---- ---- ----
It has been demonstrated that it is possible to produce such amorphous Pt structure on a porous carbon by co-deposition of Pt and carbon using plasma magnetron sputtering. [START_REF] Caillard | Deposition and diffusion of platinum clusters in porous carbon assisted by plasma sputtering[END_REF][START_REF] Brault | Anomalous diffusion mediated by atom deposition into a porous substrate[END_REF] A typical TEM image of the deposited Pt clusters is shown in Figure 5a Moreover, this result is confirmed by XPS measurements (Figure 4c) showing only the presence of PtO x H y species ( particle size. [START_REF] Brault | One-step synthesis and chemical characterization of Pt C nanowire composites by plasma sputtering[END_REF] For Pt clusters of ca. 2.5-3.0 nm, the shell Pt atoms have a +2 oxidation state, whereas the core Pt Pt atoms are metallic. [START_REF] Sellin | A thermogravimetric analysis/mass spectroscopy study of the thermal and chemical stability of carbon in the Pt/C catalytic system[END_REF] The absence of metallic Pt confirmed that the size of the clusters was small enough to consider all Pt atoms as surface atoms. [START_REF] Henry | Size Effects on Structure and Morphology of Free or Supported Clusters[END_REF] All these physicochemical characterizations confirm that the structure of the Pt deposit on the carbon porous layer consists of very small amorphous clusters. [START_REF] Brault | One-step synthesis and chemical characterization of Pt C nanowire composites by plasma sputtering[END_REF] Table 3. XPS catalyst characterization data. The assignment of chemical species to the binding energy is based on data from the Handbook of X-ray photoelectron spectroscopy. [START_REF] Wagner | Handbook of X-ray Photoelectron Spectroscopy[END_REF] Binding As described in detail above, the calculated RDF and XRD patterns for the structures generated are typical for a more amorphous Pt structure. On the other hand, the experimental characterization data (TEM, XRD and XPS) confirm that Pt clusters sputtered on a porous carbon layer are very small and amorphous.

Such electrodes have been tested under H 2 /O 2 fuel cell working conditions and have shown high performance, [START_REF] Cavarroc | Performance of plasma sputtered Fuel Cell electrodes with ultra-low Pt loadings[END_REF][START_REF] Caillard | Improvement of the sputtered platinum utilization in proton exchange membrane fuel cells using plasma-based carbon nanofibers[END_REF][START_REF] Mougenot | High Performance Plasma Sputtered PdPt Fuel Cell Electrodes with Ultra Low Loading[END_REF] particularly concerning the Pt utilization efficiency which reach ca. 20 kW g Pt -1 as shown in Figure 6. Typical fuel cell performances of hydrogen/oxygen fed fuel cells at 80°C, with 0.35 mg cm -2 Pt per electrode, are higher in terms of achieved power densities, ca. 1.0 to 1.2 W cm -2 with oxygen pressure between 1.0 and 3.0 absolute bars [START_REF] Kadjo | Improvement of proton exchange membrane fuel cell electrical performance by optimization of operating parameters and electrodes preparation[END_REF] ,

but leads to a much lower Pt utilization efficiency of ca. 2 kW g Pt -1 . However, the stability of such small particles could be an important issue for the system as a whole. On the other hand, such structures, consisting of strongly agglomerated Pt clusters (i.e., as if Pt clusters are supported by Pt clusters) could increase their stability towards corrosion (due to a higher chemical potential [59]) and minimize that of the support (due to less surface contact). The power density and stability issues as well as the operating conditions of the cell may be not realistic for transport applications, where potential duty cycles and start-stop cycles may drastically deteriorate the fuel cell performances, but such low platinum loading system could be used for stationary or nomad applications.

Conclusion

In conclusion, plasma sputter deposition experiments have lead to high performance Pt/C fuel cell electrodes. Careful analysis of the catalytic phase allowed concluding that the catalyst consists in very small amorphous platinum clusters. For understanding this phenomenon, we have carried out molecular dynamics simulation under conditions closely matching these experiments. MD simulations demonstrated the formation of Pt clusters wetting the surface and which fit closely the surface morphology, which leads to a smooth ultrathin film. In this case, only the surface structure remains crystalline to some extent. The resulting Pt morphologies are in agreement with experiment of Pt sputtered onto fuel cell electrodes as revealed by comparing the RDF and XRD simulated patterns to the experimental XRD, XPS and TEM results. This confirms that small amorphous Pt clusters are able to grow on carbon grains and to present high catalytic activity.

Figure 1 .

 1 Figure 1. Snapshots of Pt deposition on the porous carbon substrate. The green spheres represent C-atoms and the brownish spheres represent Pt-atoms.

Figure 2 .

 2 Figure 2. The Pt concentration profile for the three sets of kinetic energies. The values in the

  RDF. Both features are representative of disorder. On the other hand, close inspection of the snapshots in Figure1reveals some atomic ordering, and specifically the formation of centered hexagons on the surface.

Figure 3 .

 3 Figure 3. The calculated RDF of the Pt deposit grown on the porous carbon.

Figure 4 .

 4 Figure 4. The simulated XRD intensities vs. 2 of deposited Pt structures on the model porous carbon substrate. Diamond symbols give the Pt bulk positions.

  with the related size distribution in the inset of Figure 5a, and the experimental XRD pattern recorded on such magnetron sputtered electrodes in Figure 5b. The TEM image shows very small Pt clusters of ca. 1 nm, and the size distribution leads to an estimate of the mean size of Pt particles wetting carbon spheres of about 1.4 nm. Note, however, that the counting is complicated due to the Pt cluster agglomeration. It is therefore likely that the bigger particles are actually agglomerated clusters rather than isolated clusters. The XRD pattern shows no diffraction peak corresponding to the fcc structure of platinum, but only a featureless Pt background, which is consistent with the very low Pt loading (10 μg cm -2 ) and an amorphous structure. Most apparent peaks come from polytetrafluoroethylene (PTFE) particles present in the porous carbon layer acting as substrate for the deposited Pt clusters.

Figure 5 .

 5 Figure 5. (a) typical TEM image of Pt nanoclusters deposited by plasma sputtering on a carbon porous layer, (b) Experimental XRD pattern showing the amorphous structure of the Pt cluster deposited onto a carbon porous layer and (c) XPS spectra of the Pt 4f orbital of Pt nanoclusters deposited by plasma sputtering on a carbon porous layer (loading: 10 µg Pt cm -2 ).

Figure 6 .

 6 Figure6. U cell vs j and P vs j curves obtained at 70 °C with a membrane electrode assembly (MEA) consisting in a Nafion 212 membrane sandwiched between symmetrical 0.010 mg Pt cm -2 Pt /CPL electrodes (flow rates of 350 cm 3 min -1 for O 2 and 500 cm 3 min -1 for H 2 ; T O 2 = 40 °C, T H 2 = 80 °C, P O 2 =4 bar, P H 2 = 3 bar).

Table 2 .

 2 The 2 position of XRD peaks for Pt crystal and simulated Pt structures (Unit: 2θ /°).

		Pt(111) Pt(200) Pt(220) Pt(311) Pt(222) Pt(400) Pt(331)
	Pt bulk crystal 39.75	46.25	67.45	81.25	85.7	103.5	118.15
	Pt (1 eV)	40.56	----	73.95	-

Table 3 )

 3 in Pt clusters, which is consistent with a very small

Acknowledgements

The financial support of the European Commission under the FP7 Fuel Cells and Hydrogen Joint Technology Initiative grant agreement FP7-2012-JTI-FCH-325327 for the SMARTCat project is gratefully acknowledged. China Scholarship Council is acknowledged for grant #2009 60212